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CHARTING DIRECTLY FROM NATURE 

From observatinns Just niatlf througli alidade traiUL-d on telemeter rod at one of the rod- 
men's statiims. the distance and bearing of that station are determined. Reduced to scale, 
this data corresponds to a line of dellnlte length and direction, whicli the topographer is liere 
shown drawing directly on the plane-table sheet. 



Sur^ eying 



A Manual of 

PRACTICAL INSTRUCTION IN THE AUTOF PLANE SURVEYING, INCLUDING 

PLOTTING, LEVELING, I'UI ANGULATION, LINE RUNNING, 

CUOSS-SECTIONING, Tl-t AVE USING, AND OTHER 

DETAILS OF FIELD WOKK 



By ALFRED E. PHILLIPS, C.E., Ph.D. 

Professor of Civil Enfrineerine, Armour Institute of Techuolocy 



ILLUSTRATED 



CHICAGO 
AMERICAN SCHOOL OF CORRESPONDENCE 
I, ific 






Copyright 1010 by 
Amkrican School of Correspondkncb 



Entered at Stationers' Hall, London 
All Rifrhts Reserved 



^ 



CciAiGia: 



y/9-;^a^5^ 



Foreword 




X ivcent years, sufli marvelous advances have been 
niaile in the engineerini;- and seientitic tields, and 
so rapid has been the evolution of mechanical and 
constructive processes and methods, that a distinct 
jieed has been created for a series of practical 
loorliing {/t/uh'.s, of convenient size and low cost, embodying the 
accunuilated results of experience and the most approved modern 
practice along a great variety of lines. To fill this acknowledged 
need, is the special purpose of the series of handbooks to which 
this volume belongs. 



C In the preparation of this series, it has been the aim of the pub- 
lishers to lay special stress on the practical side of each subject, 
as distinguished from mere theoretical or academic discussion. 
Each volume is written by a well-known expert of acknowledged 
authority in his sjiecial line, and is based on a most careful study 
of practical needs and up-to-date methods as developed under the 
conditions of actual practice in the field, the shop, the mill, the 
power house, the drafting room, the engine room, etc. 

C These volumes are especially adapted for purposes of self- 
instruction and home study. The utmost care has been iised to 
bring the treatment of each subject within the range of the com- 



iiion understanding, so that the work will appeal not only to the 
technically trained expert, but also to the beginner and the self- 
taught practical man who wishes to keep abreast of modern 
progress. The language is simple and clear; heavy technical terms 
and the forniiilie of the higher mathematics have been avoided, 
yet without sacrificing any of the requirements of practical 
instruction; the arrangement of matter is such as to carry the 
reader along by easy steps to complete mastery of each subject; 
frequent examples for practice are given, to enable the reader to 
test his knowledge and nuike it a permanent possession; and the 
illustrations are selected with the greatest care to supplement and 
make clear the references in the text. 

C The nu'thod adopted in the preparation of these volumes is that 
which the American School of Correspondence has developed and 
employed so successfully for many years. It is not an experiment, 
but has stood the severest of all tests — that of practical use — which 
has demonstrated it to be tlie best method yet devised for the 
education of the busy working man. 

<I_ For jiurposes of reaily reference and timely information when 
needed, it is believed that this series of handbooks will be found to 
meet every requirement. 




Table of Contents 



Measurement of Lines and Areas Page 3 

Plane and Geodetic Surveying' — Elementary Problems — Guntei-'s Chain 
— Engineer's Chain — Horizontal Measurements — The Tape — Chaining 
on Slopes — Correction of Errors — Use ot Chain or Tape in Lino Run- 
ning — Field AVork of Measuring Areas — Offsets and Tie-Lines — Keep- 
ing the Field Notes — The Vernier (Direct, Hetrograde). 



Leveling Instruments and Leveling Page 26 

The Level Bubble — Locke's Hand-Level — Abney Hand-Level and 
Clinometer — Leveling Uods (Target, Self-Reading) — New York, Eos- 
ton, and Philadelphia Rods — Cross-Section Rod — Ranging Poles — 
Wye Level (Four-Screw and Three-Screw) — Line of Collimation — 
Instrumental Parallax — Spherical Aberration — Chromatic Aberration 
— Adjustments of Wye Level — Adjustment of Axis of Bubble-Tube — 
Adjustment of Vertical Axis — Replacing the Cross-Hairs — The Dumpy 
Level — Adjustments of Dumpy Level — Peg Method of Adjustment — 
Precise Spirit Level — Gurloy Binocular and Monocular Hand-Levels 
and Adjustments — Setting Up the Level — Care of the Instrument — 
Problems in Leveling — Profile Leveling — Cross-Sectioning — Slope 
Stakes. 



Land and Topographical Surveying Page 69 

Meridian Plane — Magnetic Declination — The Compass — Tangent Scale 
— Prismatic Compass — Adjustment of Compass — Angle-Measuring In- 
struments — Bearing — Course — Relocation of Lines — Bearing of One 
Line to Another — Farm Surveying — Method of Progression, of Radi- 
ation, of Intersections — To Change Bearing — Latitudes and Depart- 
ures — Testing and Balancing a Survey — Calculation of Contents of 
Surveyed Areas — ^Double Longitudes — Azimuth — Rcsurveys — Division 
of Land — True Meridian — -Determining True Meridian by Compass — • 
Surveyor's Transit — Engineer's Transit — Tachy meter — Theodolite — 
Transit-Theodolite — Adjusting the Transit — Setting Up the Transit — 
Problems in Use of Transit — Traversing — ^Meander Line — Stadia — 
Stadia Rods — Tables of Elongation, Culmination, and Azimuth of 
Polaris — Base Map of the United States. 



Index Page 133 



PLANE SURVEYING. 

PART I. 



Surveying is the art of deteriniiiino-, from lueasureinents made 
upon the ground, the relative positions of points or lines upon the 
surface of the earth and of keeping records of such measurements in 
a clear and intelligent manner so that a picture (called ])lat) maybe 
made of the lines or areas included in the survey. The records 
should be systematically arranged so that any jjersoii with a 
knowledge of surveying can use the notes intelligently. The tield 
operations consist essentially of locating points, measuring lines 
and angles, measuring areas and laying out and dividing u[) areas. 
It is apparent that Arithmetic and Geometry are essential to the 
successful application of the principles of Surveying. 

The sirbject may be divided into two parts: Plane Sui'veying 
and Geodetic Surveying. 

In Plane Surveying, the portion of the earth included in the 
survey is regarded as a horizontal plane; in other words, the curva- 
ture of the earth's surface is neglected. In the ordinary operations 
of land surveying this assumption will not cause appreciable error 
as the lines and areas dealt with are of a limited e.xtent. 

As Geodetic Surveying, on- the other hand, deals with extensive 
lines and vast areas, the effect of the curvature of the earth's sur- 
face must be taken into consideration. 

All of the operations of surveying must proceed fi'om the 
direct to the indirect. That is to say, we must first measure 
directly certain quantities upon the ground and from these calcu- 
late certain other quantities that cannot be measured directly. It 
is, therefore, apparent that all field measurements must be made 
with the utmost care, consistent with the nature of the problem 
involved, and that habitual inaccuracy and slovenly methods of 
keeping field notes must be avoided. Full details accurately 
measured and carefully and systematically recorde.d should be the 
aim of every engineer who would ultimately achieve success. 



PLANE SURVEYING 



JVleasurement of lines. Probably the most elementary prob- 
lem that presents itself is to measure the horizontal distance be- 
tween two points without the use of instruments. 

This can best be done by pacing, provided both points are 
accessible. In order to make this method of measurement efficient, 
it is necessary to determine as accurately as possible the length of 
one's pace. To do this, lay off upon firm, level groiind by any 
convenient method, a line from 5U to 100 feet in length. Pass 
over this line from end to end, back and forth, keeping careful 
account of the nuuiber of steps taken each time the distance is 
covered. The total distance traversed, divided by the total number 
of steps will give the average length of one's pace. In thus 
ascertaining the length of the pace do not atteuipt to cover three 
feet at every step. It is better to adopt a natural, swinging gait. 

Having thus determined the length of one's pace, the distance 

between two points may be measured approximately by walking 

in a straight line from point to point 

and counting the number of steps. 

. . ^.^i^ This number multiplied by the length 

^A ^Tp H . . 

T"^ I of stc|) will give the length of line 

required; If the intervening space 
between the points cannot be trav- 
ersed, as for instance when the two 
j)oints are on opposite sides of a stream, the width of the streaui may 
lie ascertained ajjproximately by stationing an obsei'ver on each 
side and noting the time elaj)sing lietween the flash of a ])istol 
and the sound of the rej)ort. This interval, in seconds, multiplied 
by 1,U'.K) (velocity of sound in feet per second) will give the dis- 
tance in feet. Proper allowance must be made for direction and 
intensity of wind and therefore measurements of this kind had 
best be made upon a quiet day. 

Another eleuu^ntary problem frecjuently met with is as follows: 
Required to determine the altitiade of an object such as a house or 
a tree, without the use of an instrument. 

To solve this problem, take an ordinary lead pencil and hold 
it in a vertical position aliout two feet froui the eye, the observer 
being far enough from the object for the visual angle intercepted 
by the pencil to just cover the object from top to bottom. The 




Fifr. 1. 



PLANE SURVEYING 5 

observer tlien jiiiees the distance from his position to the object. 
Tlie height of tlie object is determined as follows : 

Let A, iicr. 1, represent the position of the observer's eye; 
BC the pencil held at the distance AD from the eye; liF the object 
whose lieight is to be ascertained. All is the distance from the 
observer to the object and is to be jtaced. Then from similar 
triangles we have 

BC : EF : : AD : AIL or EF = -^^^^- 

AD 

For example, suppose the pencil is seven inches long and is 
held at a distance of two feet from the eye; the distance from the 
observer to the object being 85 feet. Then from the formula 

EF = -^^5 = 24.8 feet nearly. 

In this, as in other problenir;. all (piantities should be reduced to 
the same units. 

The examples just given must be understood as illustrations 
merely and the student should avoid slij)shod methods ; under- 
standing that his best eiforts will be ueeded in all surveying prob- 
lems, and that the best is none too good. 

SURVEYING WITH INSTRUMENTS. 

Qunter's Chain, so called from the inventor, is well adapted 
to all classes of problems involving the calculation of areas from 
lines measured in the field. For many years this chain has been 
the English linear unit for all land measurements. It should bo 
made of steel; it is ()C> feet or 4 rods in length and has 100 links, 
each 7. '.12 inches. The handles are fitted with swivels to prevent 
the chain from kinking, and at every tenth link from either end is 
attached a brass tag with 1, 2, 3 or 4 prongs to assist in u>ieasuring. 
Thixs the tag of four prongs indicates 40 links from one end, (See 
Fig. 2| but it represents 60 links from the other end; therefore 
care miist be exercised in measuring, or distances may be measured 
from the wroncr end of the chain. The 50-link mark is round 
in form so that it may be easily distinguished from the other tags. 
Since the parts are called links, the length is expressed in chains 







PLANE SURVEYING 



ami links; it is written thus: 15 chains and 82 links is 15.82 
fliains. 

It is true that this chain is rapidly going out of use, yet cue 
should be thoroughly accjuainted with it, because many of the land 
records in this country are based upon it. In comj)nting areas, 
tlie chain has the advantage that square chains are easily reduced 
lo acres by simply moving the deciminal point one place to the 




Fig. 2. 

left; for I'xaniple. a chain is Oli feet; the S(juare would be()()X<36 = 
4:i5() s(juare feet, wliich is ,'„ of an acre. A rectangular lot hav- 
ing two sides of 0.82 hiuI 2.15 chains respectiveh'' = 13.5'' SO 
s(juare cliains or 1.3588 acres. 

QUNTER'S OR LAND MEASURE. 

7.'.t2 inches 1 link 

100 links or <)(> feet or 4 rods 1 chain 

10 s(juare chains or 4 i-oods 1 acre = 485()0 square feet 

(i40 acres 1 square mile 

A two-rod or half chain is sometimes used instead of the full 
Gunter's chain. Its only advantage is in the convenience of hand- 
ling a shorter chain when workingover uneven ground. Formerly 
the engineer's chain was almost universally employed in making 
surveys for surface canals, sewers, water- works systems, etc. It 
differs from the (iunter's chain in that is 100 feet in length and con- 
tains 100 links, each of which is, therefore, 1 foot long. 

The unit of linear measure in tlie United States is the foot. 



PLANE SUEVEYING 



In nieasuriug Hues, a chain 100 fe6t long, divided into 100 links, 
is now in nse. Distances are recorded in feet; decimals of a foot 
being nsed when possible. In cities where accurate and precise 
measurements are necessary, various kinds of tapes are nsed having 
the foot divided decimally. 

It has been decided both by custom and law that the length of 
the boundary lines of a field is not the actual distance on the surface 
of the ground, but is the projection of that distance on a horizontal 
plane. The area of a field is not the exposed superficial surface, 
but as above stated, the projection of that surface on a horizontal 
plane. For this reason, in all land sui^eying, horizontal dis- 
tances are to be measured and from these the areas computed. 

The Gunter's chain, as well as the engineer's chain, is a very 
inaccurate device for measuring distances and areas unless special 
precautions are taken to counteract the errors to which it is liable. 
Some of these errors are cumulative and some compensating, and in 
what follows no attempt will be made to classify them. Some of 
the causes of errors will be pointed out and the surveyor should 
do all in his power to eliminate them. 

The chain will sag between supports and thus the distance 
measured will be too short. This is sometimes allowed for by 
making the chain a given amount longer than the standard. Again, 
the chain may be standard under a certain pull and temperature, 
and for very precise work a spring balance is attached to one end 
of the chain to register the pull. A thermometer also is provided 
but is of little value from the fact that the temperature of the 
chain may vary considei'ably from that of the atmosphere. Still 
further, the length of the chain is likely to be increased from the 
wear of the links and connections. Each link with its connec- 
tion has six wearing surfaces so that if each surface is worn away 
but yij- inch the chain will elongate 6 inches. The rings and 
loops at the end of the links are frequently stretched out of the 
triie form, thus elongating the chain; or the links may become 
bent, thus shortening the chain. In pulling the chain over the 
ground the links and rings have a tendency to collect weeds, mud, 
etc., and thus shorten the chain. In cold weather, ice and snow 
may collect in the joints with the same result. In using the chain, 
the links and rings kink and twist, and a sudden jerk may break 



PLANE SUEVEYING 



the chain. For these reasons the chain is not at jiresent used as 
much as t'ornierly. 

The Tape. Tapes are made of various materials and are known 
as linen, metallic and steel. 

Linen tapes, from the nature of the material, are likely to twist 
and tanfrle and when wet are easily stretched; for these reasons 
they do not long retain their standard length. They are used only 
in the roughest kind of work. Metallic tapes have a linen body 
with threads of copper or bras,s running throughout their length. 
These metallic threads prevent twisting and tangling and in a gen- 
eral way assist in preserving the standard length of the tape. They 
are lietter than linen tapes but not suitable for "good" M'ork. 

Steel tapes are of two kinds, "ribbon" and "band." Ribbon 
tapes are made of thin steel about | inch wide. They are usually 
made in lengths of 50 or 100 feet. They are divided into feet, 
tenths and hundredths of a foot, the divisions being etched upon 
the tajie. The other side of the tape is sometimes divided into rods 
and links to ada])t it to land surveying, and it is either wound up 
into a leather case or upon a reel. 

Ribbon tapes are generally used when considerable accuracy 
in measurements is required, such as laying out foundations for 
buildings, bridge ])iers, measuring up sewer lines, etc. From the 
nature of their construction, they will not stand much wear and 
tear, and ai-e therefore not adapted to the rough usuage of general 
field work. If carried in the case or I'eel, on account of the sharp 
bend at the center, the tape will soon break oif at that point. 
After use in the field, the tape should be carefully wiped off and 
oiled if necessary, as the rust will obliterate the graduations and 
make it ditiicult to read. Li using the ribbon tape in the field, 
care must be exercised to jirevent twisting and kinking or catching 
iinder sticks or stones, as a slight jerk will break it. 

The band tape is best adapted to general field work and to 
rough usage. It is made of lieavy steel about y',, of an inch wide 
and 100 feet long, divided into feet; usually the first and last foot 
are divided into tenths. The one-foot divisions may be marked 
by rivets, although the rivets tend to weaken the tape. They are 
sometimes marked l)y solder, which is notched at the proper point 
and stamped with the number. They are usually fitted with light, 



PLANE SUEVEYING 9 

detachable handles for use in the field, but these are easily displaced 
or often lost in dragging the tape over stones or through grass. It 
is better to tit the tape with leather handles large enough to easily 
go over the hand. After use. the band tape should be gathered 
lip in loops about three feet long and tied in the middle forming a 
figure eight. If it is desirable to wind the tape upon a reel, there 
are at present upon the market, several styles of reels, stiff in con- 
struction and convenient to carry. 

The tajie, like the chain, is likely to change 
iu length due to changes of temperatures, and 
unless the proper pull is applied to the ends 
it will measure short of the standard. Al- 
together it is more accurate than the chain and 
of late years has largely replaced it for all 
kinds of field work. Indeed, with proper 
])recautions, it has been found possible to 
obtain nearlv as accurate results as with the 
most elaborate apparatus designed for meas- 
uring lines. 

Since the methods of using the chain in 
the tield are the same as for using tlie tape it 
will be sutticient to explain the methods of 
using the latter. The Tape. 

In connection with the tape there should be provided a set of 
eleven marking pins from 15 to IS inches in length. To each pin 
should be attached a piece of red fiannel to prev.'ut its being over- 
looked in the gi-ass. There should also be provided two rods 
(called flags), from 6 to 8 feet in length divided into foot lengths 
and painted alternately red and white. These rods are sometimes 
constructed of straight white pine, but |-inch gas pipe fitted M'ith 
a steel shoe is better. It is desirable also, to provide a plumb-bob 
and string;, and a hatchet. 

Use of the Tape or Chain. For measuring a line with the 
tape, two men are required, a "leader" and "follower," or head 
and rear taperaen. The first step is to set one of the fiags at the 
far end of the line to be measured, or if the line is too long, only 
as far ahead as can be distinctly seen. It is best to mark the 
beginning of a line with a stake driven as closely to the ground as 




10 PLANE SURVEYING 

circumstances will permit. The tape is then unrolled or unfolded 
in the direction of the line, the lOO-foot mark going ahead. The 
leader takes the pins and the forward end of the tape and with a 
flag walks off in the direction of the forward end of the line, 
dragging the tape after him. When nearly one hundred feet away 
the follower cries "■ down " and the leader faces the follower holding 
the Hag vertically to-be signalled into line by the follower. The 
tape is then stretched and straightened and a pin stuck vertically 
into the ground exactly at the lOO-foot mark. The leader then 
picks u]) his end of the tape and starts off as before, the process 
being repeated each time, except that the follower must be particular 
to pick up each pin that is left in the ground by the leader. 

If the line is more than eleven tapes in length, after the 
leader has stuck his last pin he cries "pins" and the follower 
delivers to him the ten pins that he has picked up. If the line to 
be nieasurtni is very long, some method should be adopted for 
keeping count of the number of times the pins have been exchanged. 
If the line ends with less than the length of a tape, the leader pulls 
out the tape to its full length, not sticking a |)in, however, and 
then walks back and notes the distance from the last pin to the end 
of the line. This distance added to the nuniber of pins held by 
the follower, including the last one stuck, will give the distance 
from the point at which the pins were exchangefl. For instance, 
if the follower has six pins and the end of the line is 65 feet from 
the last pin, the entire distance from the point of exchange of pins 
is fjlio feet. It must be remembered that each exchange of pins 
counts for 10 tape lengths or l.OOU feet. 

Chaining on Slopes. One of the most important uses of the 
chain is to measure accurately distances where the surface of the 
land is uneven or of a sloping nature. In measuring up or down 
a slope, one end of the tape is raised until the top is as nearly as 
possible in a horizontal plane. If the slope is too steep to permit 
of one end of a full tape being raised enough to bring the tape 
horizontal, the tajjc is ''broken," that is to say, only a part of the 
tape is used at each measurement. To do this the tape should be 
stretched to its full length, the leader returning to such a point 
upon the tape that the portion between himself and the follower 
may be properly leveled. A measurement is made with this por- 



PLANE SURVEYING 11 



tion, the operation being repeated witli tlie next section of tape and 
so on until tlie entire tape has been used. Care sliould be taken 
not to eonfuse the pins. The liigli end oi' the ta[)e may be trans- 
ferred in any one of several ways, depending upon the degree of 
aceuraev recpiired. For great accuracy, a ]iluuil)-bob should be 
used but it should not be dropped and the ])in phiced in the hole 
made. It should be placed about where the bob will drop and the 
grass should be tramped down and the groiiud smoothed. The 
bob should then be lowered carefully until it almost touches the 
ground and allowed to come to rest. Then lower it until it reaches 
the ground when the pin should be stuck in the ground slantwise 
across the line exactly at the point of the bob. If less accuracy is 
permissible, it may be sutHcient to drop the ])iii, ring end down 
and note where it strikes the ground, or a ])ebble may be dropjjed 
in the same way. In measuring njihill, the follower must hold the 
bob directly over the pin in the ground while he aligns the 
leader and sees that he sticks the pin while the bob is directly 
over the point in the ground. It is much easier to measure down 
than up hill so that when close measurements are required on 
slopes, the measurement should, if possible, be made down hill. 
Even under the most favorable conditions measurintr lines with a 
tape is a most difficult operation for experts, and beginners cannot 
expect to attain efficiency except by constant |)ractice and careful 
attention to every detail that will tend to eliminate error. For the 
method of chaining up and down hill, see Fig. .'5. 

Let it be required to find the distance AM, at which ])oints 
two hubs have been estal)lished. Let A B (! D E F, etc., be the 
points of the successive chaining and <i h c <l, etc., the horizontal 
planes. Starting from the point A; sup[)ose the surface between 
A and B to be of no great difference in elevation, therefore, the full 
length of the chain can be used between these two points. The 
head chainmau goes to the point B, and holds the head end of the 
chain on the ground, while the rear ehainman holds the zero end 
at A and with aid of the plumb-bob "plumbs down," thus chain- 
ing the distance horizontal. This distance measured, the head 
ehainman establishes a peg in the ground and calls out the dis- 
tance "One hundred" or station one, then goes to C, which rairst 
be approximately low enough to allow the rear ehainman to con- 



12 



PLANE SURVEYING 



veiiieiitly jilumb down to I>. In this case the slope of the hill is 
greater than that between A and B, thus the inipracticability of 
using the full length of the chain is apparent. This distance, 
therefore, is taken at a fractional ]>art of the chain, as before stated, 
called "breaking the chain." The distances at such breaks should 
always be taken at an even number of feet whenever possible and 
at distances that are easily remembered, as 10, 20, 25, 50 feet, etc. 
The leader in every instance calls out the distance of such "breaks" 
and the rear chainman goes to the next peg and holds off the num- 
ber of feet j)reviously called out. Now as the distance A B is 100 
feet and the distance B C 40 feet, the head chainman at C calls 
out "1 2>lus 40," meaning 140 feet from A. He ne.xt goes to D and 
the rear chainman calls out the distance measured "1 plus 40" and 
holds olf 40 feet at /^ and plumbs down to ('. In this case the 
leader also plumbs down from <■ to D. This method is continued 




Fig. 3. 

until M is reached, using the system df 1, 2, 8, 4, etc., plus the 
fractional measured distance, instead (if using the whole number, 
as 125, 225, etc. The rear chainman should gather the pins after 
a new point has been established. As already stated the chaining 
can be checked by counting the pins jiicked uji. Always allow 
the last ])in to remain in the ground until absolutely certain it is 
no longer desired and can be of no further service. It is im- 
portant that the distances should be checked by bothchainmen as it 
may prevent serious mistakes, and in somecases prevent rechaining 
the entire distance. Distances in ])laces where angles are taken 
are sometimes checked in the oftice by Trigonometry. 

A few hints in regard to the use of the tape may not come 
amiss. 

Always measure to and from the same side of a ])in. 

Hold the end of the tape as near the ground as possible. 

Before sticking the pin, be sure there are no kinks in the tape 



i'LANE SURVEYING 18 

and that tlif ta])e is not tietlected to one side liy grass, sticks or 
stones. 

Never straighten tlie tape witli a jerlc; raise it clear of the 
ground and straighten and stretch with a steady jmll and k>\ver 
steadily into place. 

The tape man should never bi-ace himself against a pin; he 
should assume a position of stable equilibrium, preferably with one 
hand upon the ground. 

In passing over uneven ground, every reasonable effort should 
be made to hold the tape level. Too much time should not be 
spent in attempting to hold the end of the tape exactly over the 
jioint in the ground when the difference of level of the ends of the 
tape is sufficient to neutralize what would othervrise be considered 
an accurate measurement. 

In passing over rough ground the tape should be carried free 
from the ground, thus saving it unnecessary wear. The length of 
the tape is likely to vary from time to time, from changes in tem- 
jjerature, from constant stretching and froni accident in the field. 
For this reason the surveyor should compare frequently the lengths 
of his tapes with that of a standard. The length of the standard 
tape may sometimes be conveniently laid off upon the floor of a 
building, or two monuments may be set in the ground, the proper 
distance between them being measured either by a standardized 
tape or by means of wooden rods. Having found the error in the 
length of the tape the necessary corrections can then be made. If 
a line has been measured upon the ground, and it is afterwards 
found that the length of the tape is in error, the true length of 
the line may be found from the following proportion: the true 
length of the tape is to the length of the standard tape, as the true 
length of the line is to the length of the line as measured. 

Suppose a line as measured, is found to be 625 feet in length 
and it is afterwards found that the tape is too long, by six inclies. 
Then we have: 100.5 : 100 :: x : 625 
from which ./• =; true leno-th of line = 628-A- feet. 

EXAMPLES FOR PRACTICE. 

1. A line as measiired with a certain tape is 580 feet in 
length. It is afterward found that the tape is ^^ of a foot too 
short. Determine the true length of tlie line. Ans. 578.26 feet. 



14 



PLANE SURVEYING 



was i foot too lonjj. 



2. A line is known to be 840 feet in length, bat when meas- 
ured with a certain tajie is found to be 842i feet in length. Deter- 
mine the true length of the tajie. 

Ans. 90.7 feet. 

3. A certain field was measured with a Gunter's chain and 
found to contain 625 acres. It was afterwards found that the chain 

Determine the true area of the held. 

Ans. ()28.1;3 acres. 
If an area has been measured with a certain tape that is after- 
wards found to be in error, the corrected area may be found by the 
following proportion: The square of the true length of the tape is 
to the square of the length of the standard tape as the true area is 
to the measured area. 

Examples will now be given illustrating the use of the chain 
or taj)e, in the held. 

1. To erect a perjyendicular at a given imitit in a line. 
Let AH Fig. 4 be the given line and C the point in the line at 

which it is desired to erect a perpen- 
dicular. Since a triangle formed of 
the sides 3, 4 and 5 (or any multiple of 
these I will contain a right triangle, take 
parts of the chain or ta2)e representing 
these distances or multiples and have 
the angle included between the shorter 
sides at C". Therefore, fasten one end 
of the tape or chain at E, 30 links or 
feet from C and the iJOth link or foot 
at C. Then with the 5U-foot mark in one hand, walk away from BC 
until both of the segments DE and DC are taut. Stick a pin or 
stake at D and DC will be the perpendicular required. If the 
])erpendicular should be longer than can be laid out with the tajie 
or chain, lay out CD as described and align a "riag"' from C to D 
produced. 

2. To let fall a perpeiulicular to a given line from a given 
point outside the line, (a) "When the point is accessible: 

Let AB Fig. 5 be a given line and C a point. From C as a 
center, with any convenient length of tape or chain as a radius, 
describe the arc DE, cutting the given line at points D and E. 
Stick pins at D and E and measure the distance. Bisect this dis- 




Fig. 4. 



PLANE SURVEYING 



15 



tance at F; then CF will be the jierpeiulicular re(]uired. If the 
line AB is too far from (.' to be reached with the chain or tape, it 
will be necessary to range out a line conveniently near to (' which 
shall be parallel to AB. To do this erect at any convenient point 
on AB, as at N, Fitj. 6, the perpendicular, and prolong it as far as 
necessary, as 11. At R, erect KS perpendicular to EN. Then the 
perpendicular let fall from C upon liS and prolonged to ^iB will 
be perpendicular to AB. 



Fig. 5. 



Fig. 6. 



(b) "When the ])oint is inaccessible: Let AB, Fig. 7, lie the 
given line and (' the inaccessible point from which it is desired to 
drop the perpendicular to the 
line AB. At any convenient 
point F in AB erect the per- 
pendicular FD and extend FD 
to E, so that FE=FI). Locate 
the point B so that B. D and C 
will be in the same straight line. 
Sight from E to (' and find the 
point II in which this visual line 
crosses AB. Next find the point 
G at the intersections of DII and 
BE prolonged. Sight from G to 
C and the point M in which this 
visual line crosses AB will be the 
point required and the distgyice 
MG will equal 51 V. MC will be 
the perpendicular to AB at M. 

3. T/irough a given 2)oint to run a line that _xhall ho 
parallel to the given line. The given point and given line being 
accessible: Let C, Fig. 8, be the given point and AB the given line. 




Fig. 7. 



16 



PLANE SUKVEYING 



From point C let fall CD perpendicular to AB. At C erect CF 
perpendicular to CD; then EF will be the parallel required. 

4. To j)i'(ihiii(i (I It III' hi'ijond an olmtade. Let AB, Fig. 9, 
be the given line which is intercepted by a tree, house or other ob- 
stacle. It is recjuired to locate the line ('D which will be in the 
direction of .AB produced. At B erect BE perpendicular to AB 
of sufficient length to clear the obstacle and at E erect EF perpen- 
dicular to KB proh)nging EF beyond the o1>stacle. At F and C 
erect perpcndicnhirs to EF and VY making CF^ equal in length to 
BE, then CD will l»e the line required and the distance from A to 
D will e.pial AB plus EF plus CD. 




Fig. 8. . Fig. 9. 

5. Whin both ends of a line are accessil/le, but the line 
cannot bf nii'iixnrnl ihrcrtl if, on iircoiint of olmtarlefi. 

At each end of the line (Mvct pci'peiidicnlars of equal length 
sufficient to clear the oiistacles, and nieasnre the length of the line 
i)etween the extremities of these jierpentlicnlars. 

0. Wlun both ends of a line are accensible, but neither can 
be Kienfroni the, other, thiiK jtri'venting direct uVujn inent. 

Such a case occurs when it is desired to run a line across a 
wooded field, the trees and un- 
derbnisli preventingthealign- 
ment of the intermediate sta- 
tions. Let AB Fig. 1(» be the 
line whose length is desired. 
From A run a line AB' (called 
a random line) in any coii\en- 
ient direction and continue it till the point B can be seen from B'. 
.\t B erect the ])erpeudicular !!!>' to AB and measure BB'. Then 
from the riifht anifleil trianolc .VBB'M'e will have 




Fig. 10. 



AB= 



^=iJab''_ 



BB' 



PLAXE SniVEYIXG 



17 



The distance from A to any intermediate station as C can be 
fouiui bv measuring the length of the perpendicular CC to AB. 
From similar triangles we have 

AC : CC'::AB : BB' 
CG'XAB 



AC 



BB' 



7. To locate j^oinfx in a line over a hill, hofh ends of 
which are visible from points near the summit. 




Fig. 11. 
Set a flag at each of the points A and B Fig. 11. One man 
then goes to D, as closely in line with A and B as can be esti- 
mated. He then signals a man at (_' in line with A. (! then 
signals D to D' in line with 
B. \y signals C to C in 
line with A and so on alter- 
nately until the points C" and 
D" are reached in line with 
A and B. 

If the points A and B can- 
not be seen from the toj) of 
the hill, run a random line 
over the hill as described in 
problem 6 and offset to the 
true line. 

8. To locate ])'^'vn'ts in a line across a wicle^ deep valley, 
the extremities of the line being visible from each other. 

Fix a point C, Fig. 12, on the edge of the slope in line with 
A and B. Then holding a plumb-line at C and sighting across 




Pig. 12. 



18 



PLANE SURVEYING 




Vig. ].-?. 



to B the iiiteriiiediate points D, E, F and (_' can be put into line. 

1. The Field Work of Measuring Areas. Zet tis con- 
sider the trhi injuliir JieUJ AJiC, I^iij. 1-i. Beginning at any 
convenient corner as A, measure from A to B, then from B to C, 
and finally from C to the point of beginning. Should a stream 
cut across the field as shown, measurements should be made from 
the corners to the points where stream crosses the boundary lines. 

Should it be found impossible to measure the 
sides of the field directly, owing to zigzag 
fences or other obstacles, offset parallel lines 
as in the figure and measure the length be- 
tween such parallels. 

The area of the figure may be found from 
the following rule: From one-half the sum of 

o 

the three sides, subtract each side separately. 
Multiply together the half sum and the three 
remainders and extract the square root of the 
product. Thi.s lule is explained in Art. 198 of Elementary Alge- 
bra and ^[ensui'ation. 

1 r tlie lengths of the sides are given in chains, the area will 
be given in scjuare chains. If the lengths of the sides are in feet, 
the result will be in scjuare feet. 

2. 7'" K'in'ii/ a f(i}ir-sided field xoith the tape or chain. 
Pleasure around the field in the same way as before, but in 
addition, it Mill be necessary to measure a tie- 
line'lK'twci'ii two opjiosite corners, thus dividing 
the figure into two triangles, the sum of whose 
areas \\\\\ give the area of the entire figure. 
Such a tic-line is shown in Fig. 14 by the dotted Of: 
line Dl!. If neither of the diagonals DB nor 

o 

A(" can be conveniently measured, measure the 
short tie-line LS for instance, and the distances 
C'S and CL. Then in the triangle LC'S the 
three sides are given, from Mhich to find the 
angle I.CS. Having this angle, we can calcu- 
late the length of 1)1! and therefore the area of the two triamdes 
composing the field. 

If it is not convenient to measure the tie-lines inside tlie field. 



Mr 



-7N 




PLANE SURVEYING 10 

two adjacent sides as BA and DA can be prolonged to M and N 
forming the tie-line MN. It ■will iisnallj be found more convenient 
to lay otf CS er^iial to CL, thus forming an isosceles triangle, 

3. To suntc'v a five -sided field with the tajye or chain. In 
this case two diagonals as EB and BD, Fig. 15, or two tie-lines aa 
- s and mil must be measured in addition to the lengths of the 
sides. "Whatever the number of sides, a sufficient number of 
diagonals or tie-lines shoiild be measured to divide the area into 
triangles from which the area of the entire field may be calculated. 
If N represents the number of sides of a field, there will be 
required N-3 diagonals or tie-lines, form- 
injj N-2 triangles. 

To simplify calculations when tie-lines 
ai'e used in place of the long diagonals, 
the following method may be adopted: 

Measure off A.111, any fractional por- 
tion of AE, and An the same fractional 
j)ortion of AB and measure iiitt. Then 
mil will be to EB as A.m is to AE or as A.a 
is to AB. Suppose for example that Km 
is J,j^ of AE and A// is J^- of AB. There- pj,, 15 

fore EB is 10 times the leuo"th of mii. 

o 

EXAMPLES FOR PRACTICE. 

1. Given the three sides of a field as 5.2.5, 6.50 and 4.00 
chains. Find the area of the field in acres, and square rods. 

Ans. 1 acre, iU.US square rods. 

2. Given CB=3.()5 chains, 00=2.85 chains, (\=:C,'=0.50 
chains and < .v=0.()5 chains.* Calculate the area of the triangle 
BCD. Ans. 5.11 S(]nare chains area. 

Off=sets and Tie=lines. To find the area of a field which is 

Ixninded in part by a stream, it is necessary to use off -sets, as 

follows: Measure the sides of the field in the usual manner and for 

the irregular boundary run a straight line, as ED, Fig. 16, and 

calcixlate the area of the field included between these boundary lines. 

To this area must be added the area included between the line ED 

and the irregular boundary. 

*Note: In all problems involving the measurement of land, the chain 
referred to is the Gunter's chain of 66 feet, unless otherwise noted. 




20 



PLANE SUKVEYING 



To find this area, at points aloncr ED, erect perpendiculars to 
the irregular shore line at such distances that the lines 1' 2', 2' 3' 
etc., may be considered straight. The desired area will evidently 
equal the sum of the areas of the trapezoid? ttii3 formed. The 
distance from E to any point 1, 2 or 3 on ED is called the ahscissa 
of that point and the perpendicular distances from ED to 1' 2' 3' 
etc.. are called the iiril'i mifix of the point. 




Fijr. 16. 

Instead of summing the trapezoid as above, the desired area 
may be found by the following rule: Multiply the difference 
iietween each ordinate and the second succeeding one by the 
al)scissa of the intervening ordinate. Multiply also the sum of the 
last two ordinates by the last abscissa; one-half of the algebraic 
sum of these several products will be the area required. 

To find the area of an inaccessible swamp, a lake or other 
area, run a series of straight lines entirely enclosing the given 
area, and since the diat{omils cannot be measured, measure tie-lines 
ci tiler inside or outside of the area. As already stated, calculate 
the area included between the straight boundary lines and from 
this area substract the area included between ofF-sets let fall from 



PLANE SrKVEYI^H; 



r -_ 



points npon these boiiiidarv lines. Eeference to Fig. 17 will make 
the method of ]i;'ot'edure plain. Surround the inaccessible area 
by straight lines, AB. B(\ CD, etc., and calculate the enclosed 
area. At proper intervals along 
these strai"ht lines, erect and 
measure ])erpendiculars. ex- 
tending to the edge of the inac- 
cessible area. ( 'ompute the area 
between these })erpendiculars 
by the i-ule on page 20 and for 
the re(juired area, subtract Lt F 
from the area previously found. 
Since the long diaiJonals are not 
accessible, measure the area by 
measuring the interior tie- lines ; 
remembering that the required 
number of tie-lines will be less 
by ;3 than the number of sides 
enclosinjj the area. 

Example. Given the dis- 
tances measured along the 
straight line AB(Fig. iN) with the corres-jionding off-sets measured 
to the broken line A('1)I'^. It is riM|uin'd to compute tlu^ area 
between AB and the broken line .\('i)K. 




FIk. 17. 




Fig. 18. 



Difference of 1st and .'Jrd ordinatcji 



0' — 5o'= — 50' etc. 



2nd ' 


' 4th 


.3id • 


• 5th 


4th ■ 


• Gill 


5th ■ 


■ Tlh 



Sum of last two ordinates ■ 



=40'— 35'=+ 5' 
=55'— 18'=+.37' 
=35'— 40'=— 5' 
=18'— 60'=— 42' 
= 40'+60'=l00' 



22 



PLANE SURVEYING 



Abscissa of intermediate ordinates between 1st and 3rd== 40'X — 5iy=-2200 

2nd " 4th= 90'X+ 5'= 450 

" " " " " 3rd " 5th=132'X-i-37'= 4884 

4th " 6th=172'X — 5'=- 860 
5th " 7th=2l7'X-^'=-9114 

" " last ordinate = 267' Xl00'=26700 

Oiu'-lialf the algel>raic sum of the products as given above 

will give the re(jiiired area. 

32034— 12174 ,^„^ 
Area ^= ^ = 't!(30 square feet. 

EXAHPLE FOR PRACTICE. 

1. (iiven the distances measured along the straight line AB 
Fig. A with the corresponding off-sets measured to the broken line 
ACDKKI', to find the area between AB and the broken line 
ACnEFB. Check the result by calculating the areas of the 
trapezoids and triangles of the figure. Ans. 11,S~5 square feet. 




FiK. A. 

Keepinjr the Field Notes. In kee|)ing field notes, clearness 
and fullness should he constantly ke])t in mind. As field notes 
often pass into the hands of a second party, they should admit of 
but one interpretation to a person at all acquainted with the nature 
of the work. E.xtra time spi-nt in the field in actjuiring data will 
avoid confusion and vexatious delays when the notes are worked 
u|» in the otlice. Avoid the habit of keeping notes upon scraps of 
paper or in vest-pocket note books. Provide note books es{)eciallv 
ailapted to the keeping of field records and number and index them 
so that the contents may he understood at a glance. Keinember 
that sketches made upon the ground aid materially in interpreting 
field notes that otherwise might be unintelligible. 

There are three principal methods of keeping field notes; first. 
by sketches alone; second, by notes alone; and third by full notes 



PLANE SURVEYING 3;1 

supplemented by sketclies. Tlie tliini lUftliod is without doubt 
the best, but exauiples of the others will be <i;iven. For keeping 
- the notes of the chain survey there should be provided what is 
known as a lield book, a pencil (preferal)ly 411), rubber eraser and 
and a short rule for drawing straight lines. 

J^irs/. hi/ ^^/i-efc/ics Alone. Either page of the note book may be 
used for sketching but it will be more convenient to use the right- 
hand page, as it is ruled into S([uares. thus permitting sketching to 
scale. Always sketch in 
the direction of the sur- 
vey, beginning at the 
bottom of the page and 
making the center line 
of the page correspond 
approximately with the 
North and South lines. 

Second, hij JVotes 
Alone. Use the left- 
hand page of the note 
book beginning at the 
bottom as before. Do 
not crowd the notes, and 
if necessary use two or 
more pages. See Fig. 19. 

Fig. 19 shows the 
method of keeping the 
notes of the s u rve y Fig. 19. 

shown in Fig. 20. 

Third, bij JVotes and Sketches. It is apparent that in this 
method both the tirst and second methods are embodied in the notes. 



^MZ 



— r- 

1040' 

400' 
330' 



"15~ 
500' 

c 



750 

470' 
420' 




THE VERNIER. 

The vernier is an auxiliary scale for measuring with greater 
precision the spaces into which the principal scale is divided. The 
smallest reading of the vernier, or the least count, is the difference 
in length, between one division on the main scale and one on the 
vernier. 

A vernier is said to be direct when the divisions on the 



24 



PLAxXE Sl-'liVEYJNG 



vernier are smaller than those on the main scale Fig. 21 A; retro= 
grade, when the divisons on the vernier are greater than those on 
the main scale. See Fig. 211!. 

In Fig. 22 let MM 
represent a scale divided 
into tenths; then since 
ten spaces on the vernier 
W are e(jual to nine 
spaces upon the scale, it 
is evident that each space 
upon V V is short by one- 
tenth of a space of Mil. 
The least count is there- 
fore, -,V of ,V or -j-J, . 

The vernier and slow 
motion screw of the ver- 
tical arc of the engi- 
neer's transit are attach- 
ed to the left hand 
standanl of the instru- 
ment. 

Fig. 2;} represents a 

vernier as aj)plied to an 

engineer's transit. 1 1 

will be noticed that the 

, . ,. -I I Fig. 20. 

main scale is divuietl so 

as to read directly to ;50 minutes. The vernier is so divided that 

2'.» spaces n|)()n the main scale equal 80 spaces upon the vernier, 

therefore tlie least count of the vernier is ^^^ of :5() minutes or 

1 minute. 




L 



\ 



Q i r i'i 'i 'i' i '( [ i r i' / i' i' i ' f B i i i li i ' i ' i'i ^' i' iiil 



iiiiiiii 



TTl 



I'ifj. -n. 

It will he a;>]iarent, therefore, that the readings are taken 
in the direction of the increasing graduations of the main scale. 
Thus, for e.xaniple, in Fig. 28, it will be noted that the zero </, 



PLANE SUliVEYlNG 



25 



has passed the 150th space on the main scale, and is near the 30 
niinnte (half degree) division li, therefore the coincidino- lines of 
the vernier and main scale must be between and o(l', ant! we 





1 


2 


3 


4 




5 




6 




7 


8 


9 




M 




















M 


V 






















V 



12 3 4 



5 6 

FiK. 22. 



8 9 10 



find theiu, by lookincr alonij the scale of the vernier, at 17 niinntes 
helice, the reading is 15<5'' 00' + l'3"= 150^ IT'. 




Fig. 2,3. 

Fig. 24 represents another method of division of tlie circle of 
the transit. The vernier is douljie, and ti)e figures on tlie vernier 
are inclined in the same direction as the figures on the scaie to 
which they beloncr. 




Fig. '24. 

It will lie noticed that the main scale reads directly to 20 
minutes and that the vernier is so divided that 39 spaces upon the 
scale correspond to 40 spaces upon the vernier. The least count 
of the vernier is therefore ^ of 20 minutes or fif of 1 minute 
equals 30 seconds. 

To read the inside scale, it will be noticed the zero of the 



26 PLANE SURVEYING 

vernier is beyond the 138° mark and about half way between the 
tirst and second 20' divisions. The readintr so far is then 138° 20'. 

o 

Now look along the vernier to the right until a line upon the ver- 
nier is found that seems to be a prolongation of a line upon the 
scale. This occurs at the division marked 10 upon the vernier 
so that tiie reading is 138^ 20' + 10' or 138^ 30'. 

For the outside scale, the zero of the vernier is beyond 
the 221° mark and about half way between the first and second 
20' divisions. The reading so far is therefore 221° 20'. Now 
look along the vernier to the left as before, and the divisions coin- 
cide at the division marked 10 upon the vernier, so that the read- 
ing of the outside scale is 221° 20' + 10' or 221° 30'. The sum 
of the readings of the two scales equals 360° as it should. 

EXAMPLES FOR PRACTICE. 

1. Determine the least count of the vernier in Fig. A, 89 
spaces upon the scale, being equal to 40 spaces upon the vernier. 

2. Determine the least count of the vernier in Fig. B, 50 
spaces upon the scale being equal to GO spaces uj)on the vernier. 
The figure represents what is called & folding vt: rule i'. To read it 
follow along the vernier in the usual way until the division marked 
10 is reached. If there are no corresponding lines, then go back 
to the other end of the vernier beginning with the other 10 mark 
and follow it back toward the center of the vernier. 

3. Determine the least count of the vernier of Fig. C, which 
represents the usual metiiod of dividhig the vertical circle of the 
transit. 

The Level Bubble is one of the most important attachments of 
an engineering instrument, and an instrument otherwise good may 
be rendered useless by imperfect level tubes. 

The spirit level is a glass tube nearly filled with a mixture of 
ether and alcohol, the remaining space being occupied with the 
vaj)or of ether. Alcohol alone has not proved satisfactory as it is 
too sluggish in its movements, thereby rendering an instrument 
lacking in sensitiveness. If the tube were perfectly cylindrical, 
the bubble would occupy the entire length of the tube, when hor- 
izontal, or when sliirhtlv inclined to the horizon, thus rendering; it 
impossible to tell when the tube is in a truly horizontal jiosition. 



PLANE SURVEYING 



The tube i;;, therefore, crround on the inside so that a h;)ngitudinal 
section is a seiiinent of a cirele. If tlie tube is not ground to an 
an even curvature the bubble will not travel the same distance for 
every minute of arc to the extreme ends of the tube, and an other- 
wise perfect instrument will not work well. 




A line tangent to the circular arc at its highest point, as indi- 
cated by the middle of the bubble, or a line parallel to this tangent, 
is called the axis of the bubble tube. This axis will be horizontal 
when the bubble is in the center of the tube. Should the axis be 
slightly inclined to the horizontal, the bubble will move toward 
the higher end of the tube, and the movement of the bubble should 
be proportional to the angle made by the axis with the horizontal. 
Therefoi-e if the tube is graduated, being a portion of the circum- 
ference of a circle, with a radius so large that the arc of a few sec- 



28 PLANE SURVEYING 

onds is of an appreciable len^tli, it will l)e possible to determine 
tbe angle that the axis may make at any time with the horizontal, 
provided the angular vahie of one of the divisions of the tube is 
known. This is done by noting by how many divisions the center 
of the bubble has moved from the center of the tube. 

Since divisions of uniform length will cover arcs of less angu- 
lar value as the radius of the tube increases, and since a bubble 
with aeiven bubble space will become more elongated as the radius 
is increased, the sensitiveness of the bubble is proportional to the 
radius of curvature of the tube and the length of the bubble. The 
length of tile bulihje, however, will change with changes in tem- 
iieraturc. bccominir lonirer in cold weather and shorter in warm 
weather. This is due to the fact that the li(piid in the tube expands 
and contracts more rapidly than the glass. If the bubble contracts 
e.\cessivelv, the sensitiveness is thereby impaired, and it should 
be possible to regulate the amount of liipiid in tiie tul)e. This is 
done i>y means of a partition at one end, having a small hole in it 
at the bottom. A buljble should come to rest (juickly, but should 
respond easily and (piickjy to the slightest change of inclination 
of the tube. 

To determiiic the radius of curvature of the tube, proceed as 
follows: J.et S - length of the arc over which the bubble moves 
for an inclination of 1 second. Let R = its radius of curvature. 
Then S: 27rR :: 1" : 3G0°. 

R 

From which R - 2(X)2()OXS Or =S^ . „,,....- 

2Ub2bo 

S may be found by trial, the level being attached to a finely divided 
circle. Or, brinirthe bubble to the center and si<rht to a divided 
rod; raise or lower one end of the level and again sight upon the 
rod. Call the dilFerence of the readings //, the distance of the rod 
</, and the s|)ace which the bubble moved S. Then from approx- 
imately similar iriancrles 

,/S 
''= — 

EXAMPLE FOR PRACTICE. 

1. At 100 feet distant, the difference of readings was 0.02 
foot, and the bubble moved 0.01 foot. What is the radius of the 
bubble tube ? Ans. 50 feet. 



PLAKE SURVEYING 29 

Locke's Hand Level. This iiistruiiient consists of a brass tube 
six inches long with a small level mounted on its top at one side 
of the center near the object end. See Fig. 25. Underneath the 
level is an aperture across which is stretched a horizontal wire 
attached to a frame. This frame is made adjustable by a screw 
and a spring working against each other, or by two opposing 
screws jjlaced at the ends of the level mounting. In the tube, 
directly below the level, and at -45' to the line of sight, is placed 
a totally reflecting prism acting as a mirror. The images of the 
bubble and wire are thus reflected to the eye. The prism divides 



Fig. 25. 

the section of the tube into two halves, in one of which is seen 
the bul)ble and wire focussed sharply by a convex lens jdaced in 
the draw tube at the eye end of the instrument, while the other 
permits of an open view. Putting the instrument to the eye and 
raising and lowering the object end until the bubble is bisected by 
the horizontal wire, natural objects in the field of view can be seen 
through the open half at the same time, and approximate levels 
can then be taken. To prevent dust and dampness from entering 
the main tube, both the object and the eye ends are closed with 
plain glass. 

There are two adjustments necessary in this insti'ument: First, 
the bubble tube: it should be so adjusted that the bubble will be in 
the center of the tube when the instrument is horizontal. Second, 
the horizontal wire; it should bisect the bubble when the latter is 
in the center of the tube. The methods of executing these adjitst- 
ments are so apjjarent it will be unnecessary to dwell upon them 
here. 

The instrument is intended to be carried in the pocket and is 
of especial value upon reconnaissance surveys, and for sketching in 
topography upon preliminary surveys. 

For topographical purposes, the topographer should provide 
a rod about eight feet long, divided into foot lengths, the divisions 



30 PLANE SURVEYING 

painted alternately red and white. Upon this rod, the topographer 
should mark by a notch or other means, the height of his eye above 
the ground. Standing then upon a station of the line of survey, 
the topograj)her directs his assistant to carry the rod out upon 
either side of the line and in a direction at right angles thereto, 
un^il a jioint having the proper elevation above or below the center 
line is found as determined by the topographer holding the instru- 
ment in a horizontal jiosition at the e^'e. The topographer then 
paces the distance, while the assistant carries the rod to the next 
point. It is evident that if the line of sight from the instrument 
coincides with the mark upon the rod, the two points upon- the 
ground are at the same level. If the line of sight strikes the rod, 
say one foot below the mark upon the rod, it is evident that the 
ground wliere the rod is held is one foot higher than where the 
instrument is held. These operations can be repeated indefinitely 
and made to extend as far as necessary upon either side of the line. 
The points of proper and e(jual elevation are then connected form- 
ing contour lines, but the topographer should fill in details by the 
eye. The methods of keeping the field notes will be illustrated 
and described later. 

Let BCXDEFGand II, Fig. 2(3, represent the successive rod 
readings on the right of the center line A, and B' C D' E' F' G' the 
readings on the left. Now suppose the leveler stands with a Locke- 
level at zei'o and the rod is held vertically at B. The line of sight 
ab bisects the rod at 8.6 feet. The distance from the ground to the 
observer's eye is 5.5 feet. Thus it is apparent the elevation at B 
will be 3.1 feet lower than at A. The observer now paces the dis- 
tance between A and B, and finds it to be 50 feet. The reading is 
now taken at (' on the line of sight rd which reads (i.2 feet, hence 
the elevation of (_' is .7 foot lower than B, and the distance be- 
tween 20 feet. Suppose an attempt is made to take a reading near 
D. Since the horizontal plane from the observer's eye to the 
ground does not strike the rod, it is apparejit that the rod is too 
far away, therefore it should be moved back to a point X where the 
horizontal plane <'f will bisect the rod at some division. The ele- 
vation of X having been ascertained, pace the distance CX, as in 
the former cases. This method is continued until II is reached, 
taking the rod readings at i/ /i, /'J, Z' /, //i /^ and .y // and pacing 



PLANE SURVEYING 



31 



the distance between each. The same 
method is used on the left-hand sid-e of 
the center line. However, where the 
surface of the oTouiid has an alirupt 
chanije between stations, it is customary 
to take cross sections at such changes and 
ascertain the distances between the sta- 
tions by pacing; the center line at such 
points is accepted as zero ; in the same 
manner perform the operation as if at 
a station. Where a cross road inter- 
sects the center line or any portion of the 
cross section, take readings at places that 
show an abrujit change, as the top of a 
bank, side of the road, or gutter, center 
of the road and on the other side in the 
same way and place as before. This rule 
holds good in places where small streams 
are situated. It is not necessary to tind 
the depth of the water, because the jiur- 
pose of the cross section deals solely with 
the surface. Where obstacles prevent the 
section being run at right angles to the 
center line, use the method of off-sets and 
secure the desired elevation as closely ap- 
proximate as circumstances will permit. 

The Abney Hand=Level and Clino= 
meter. This instrument is similar to the 
Locke hand-level, see Fig. 27, but the 
small spirit level mounted on top can be 
moved in the vertical plane and is clamped 
to a dial graduated upon one side into 
single degrees and upon the other into 
slope ratios, so that it is possible to meas- 
ure angles of slope. 

The adjustments of the instrument are 
the same as for the Locke hand-level. 

The instrument can be used in the field 



•T^ 



..^>4u 






CENTER LINE. 



.4,0 






09 



PLANE SUEVEYING 



in the same manner as the Locke hand-level, but is of more universal 
application. It is of especial value upon steep slopes when the effi- 
ciency of the Locke level would be limited by the length of rod. 
In using the Abuey instrument it is only necessary to mark the 
height of the eyes uj)on the rod. In sighting upon the rod, with 
the horizontal line coinciding with the mark upon the rod, move the 
vertical circle until the bubble is in the center of the tube. Read 
the vertical angle, and the tangent of this angle multiplied by the 
horizontal distance to the rod will give the diffei'ence of elevation. 
If the distance to the rod is measured along the slope of the 




Fig. 27. 

ground, multij)ly this distance by the sine of the vertical angle to 
get the diU'ereuce of elevation. 

The most satisfactory method of using this instrument is in 
connection with a straijiht edge from 8 to 10 feet in lencrth. The 
straight edge is laid upon the gi-oiind parallel to the direction of 
slope and the clinometer is then applied to it, the vertical circle 
being turned till the bubble is in the center. The angle of slope 
is then read, or better still, the slope ratio is read from the vertical 
circle. This operation is repeated at every change of slope, the 
distances being either paced or measured with a taj)e. For in- 
stance^ suppose the slope is found to be GO feet in length and the 
slope ratio as given by the clinometer is j-L. It is evident then 
that at the end of the slope the difference in elevation will be 6 




















RAILROAD CUT AT MADISON, INDIANA 

This; remarkable work of engineering, completed in 18i7, was one of the earliest notable 
railroad achievements in the Hoosier State. It opened direct communication between Indi- 
anapolis in the center of the State, with the important manufacturing and shipping center of 
Madison, in the Ohio valley, on the southeastern border. The roadbed in the cut Is not level, 
but descends over 400 feet through the hills north of Madison, almost to the level of the river. 
Few other railroad cuts compare with this in scenic attractiveness. 



PLANE SURVEYIKG 



33 



u 



feet. The instrument is sometimes titted 
with a small compass and a socket for use 
upon a tripod or Jacob staff. 

The Leveling Rod is an important part of 
the leveling outfit; it is used in measuring 
the vertical distance between the horizontal 
plane through the line of sight and the point 
upon wliich the rod is held. There are three 
forms in common use known as the New 
York, Philadelphia and Boston. They are 
made of hard wood 6i feet long, sliding out 
to 12 feet and provided with target, vernier 
and clamps. 

Leveling rods are of two kinds, the target 
and the self-i'eading. Of the target rods, 
the New Y'ork and Boston are generally used 
for precise work. Of the self-reading rods, 
the Philadelj)hia shown in Fig. 28 is in more 
common use. The self-reading rods are used 
only in connection with that class of work 
where approximate accuracy only is required; 
this form is generally read to hundredths of a 
foot and can be read directly from the instru- 
men t by the observer without the aid of the tar- . 
get, as is suggested by the name. However, 
with tha aid of the target this rod can be read 
to thousandths of a foot approximately. The 
target is used when greater accuracy is re- 
quired and when the rod is so far from the 
instrument that it cannot be distinctly read. 
The rod consists of a graduated scale di- 
vided into feet, tenths and hundredths of a 
foot, and when properly made, readings to 
thousandths of a foot can be easily taken. 
The numbers making the tenths should be 
O.Olifoot long and so placed that one-half the 
length is above and one-half below the line. The numbers marking 
the feet are 0.10 foot long and each is bisected by the foot mai'k. 



e4I 



U 



Fig. 28. 



34 



PLANE SUEVEYING 



This class of rod is painted white, the foot graduations are red and 
the tenths and hundredths are black horizontal lines. 

No attempt will be made to describe the reading of the vernier 
of either the New York or Boston rod, 
but the Philadelphia rod is so divided as 
to make its reading easily understood. 
With this rod each side of the black 
horizontal line indicates lOOths, that is, 
the lower side of thfe first black space 
is called "one," and the upper side of 
the same space is called '-two," the 
lower side of the third space is called 
"three" and so on until the tenth is 
read. 

The reading is taken without the aid 
of the target, in feet, tenths and hun- 
dredths as the case may be. The mov- 
able target has a vernier which reads 
to thousandths of a foot and is read 
from zero to ten. To read this rod, 
move the target to any convenient place 
on the scale of the rod and note where 
the vernier at zero coincides with a black 
horizontal line ; then note where a line 
of the vernier coincides with a line of 
the scale. For example, if the zero of 
the vernier is just above one foot, four- 
tenths and live hundredths, as shown 
in Fig. 2'.l, and a line of the graduation 
of the vernier coincides at 7 with a Jiori- 

zontal black line on the rod, the reading will be 1.457 as is shown 
in Fiir. 2U. If reading to the nearest 100th, the reading will be 
I.-IO. This is because the 7 naturally l)rings the zero .002 above 
the line of graduation on the rod, therefore, the zero of the vernier 
is .002 nearer the ti than the 5, hence, the reading is as above. 
Should the vernier read .002 instead of .007 the reading would be 
1.-45. It is apparent that .002 now brings the zero of the vernier 
below the line, hence it will be nearer to the 5 than the 0, thus the 




Fig. 29. 



PLANE SrRVEYING 



35 



rod reading is 1.45. Therefore, in all readings with the Phila- 
delphia rod, read the thousandths to the nearest half hundredth. 
This is trae whether or not the lines coincide. 

These readings apply only to the face of the rod or to 6i- feet. 
When the rod is extended to 12 feet, or any fractional part thereof, 
the readincr is a little different, both as to its graduation and 
vernier. The scale, of course, is the same on the face of the I'od 
when extended, except as to the vernier, which is placed on the 
back at Gi feet and the scale 
of graduation on the ex- 
tended part of the rod is also 
on the back of the extension 
which runs through the ver- 
nier, as shown in Fig. -MK 
Tlie scale of hundredths is the 
only jiart to he particularly A> 
observed, together with the 
vernier in the former. 

For example, the first 
horizontal black space e'^pials 
•■one," which is the top line 
of the foot mark. The lower 
side of the first black space is 
"two,'' and the ii])])er side of 
the same space is "three"' hundredths, and so on until the tenth 
is reached. The tenth and feet are placed the same as on the face 
of the rod. The vernier, as already stated, is a little diiferent in 
point of reading and is graduated from ten to zero, instead of zero 
to ten, as on the movable target. However, with some recently- 
made rods of this type, the scale and vernier reading is the same 
throughout. See Ficr. 31. The graduation at ten is taken as the 
zero in determining thousandths. The vernier in question is firmly 
attached to the upper end of the rod Ci^s feet, (and the extension of 
the rod runs through this vernier). The differences in graduation 
of the two sides should be carefully noted. The rod has two 
clamp screws, one attached to the movable target and the other 
near the vernier on the back of the rod. In running the rod, it 
is customary, where a target or rod reading exceeding G| feet is 




36 



PLANE SUEVEYING 



desired, to set the target at (ii feet and run the rod to its hill length, 
then move down as signalled; where no target reading is required. 
run the rod to its full extent (^12 feet) and as the face of the rod has 
a scale throughout, the reading can be taken from the instrument. 

Should the instrument not he near 
enough to enable the leveler to see 
the rod distinctly without the aid of 
the target, he should first read the 
rod through the telescope of the in- 
strument and then notify the rod- 
man at what distance the intersection 
of the cross-hairs in the instrument 
approximately bisects the rod, such 
as 3.21, which means three feet, two 
tenths and one hundredth. The rod- 
man then sets his rod to I'ead this 
distance and another sight is taken, 
being careful to have tlie rod plumb. 
Sliould the intersection of the target 
fail to coincide with the cross-hairs 
in the instrument, the leveler then 
signals, or calls out if sufficiently near 
to do so, the true rod reading, as up 
a tenth, down two hundredths, as the 

case may be, and the target isj)laced at this distance. When pre- 
cision is re(|uiri'd, this method is relied ujion only for the approx- 
imate placing of the target; the method used in this case is to 
slowly move the target by standing behind the rod and holding 
it between the thumb and finders of one hand, while the target is 
moN"ed with the other. Then the target is slowly moved by the 
signals of the observer. 

"When a slow motion with the hand above the shoulder or 
below the hip is made by tlie observer, it means that the rod 
is to be moved in that direction a fractional part, as one tenth, 
but when a quick motion is made and the hand drawn back in 
the same manner it implies that the target is to be moved just a 
trifle. In this way and by proper attention to the signala of the 
observer, the rodman can become an efficient and helpful assistant, 




Pig. 32. 



PLAKE SUEYEYIXG 



37 



tliereliy saving imuh time. AVLen the target is finally set, the 
lodnian reads tlie rt:d and calls ont the readinor to tLe observer, 
when within reasonable distance. The taroet rods are read en- 
tirely by the rodnian, and the readings are kept by him in a note 
book for that purpose; these notes should be given to the observer 






=w= 


pj d 


1^ 




™, 






c 

Fig. .3.3. 




at every opportunity and results checked. To obtain correct re- 
sults when leveling, it is absolutely essential that the rod be ver- 
tical and the rodman should remember to hold the rod in this 
position. 



38 PLANE SiTEVEYINa 

The observer or leveler, Ijy iiieuiis oF the vertical wire upon 
the tarcjet of an ordinary leveling rod, can tell whether or not a 
rod is vertical and in a position at right angles to the line of sight, 
Imt he is not al)]e to determine whether the top of the rod is in- 
clined towards the instrument or in theo])posite direction; because 
when looking through tlie telescope of a level he can see only a 
fractional part of the rod. Therefore the necessity of overcoming 
this difficulty led to the invention of the bent target whicli obviates 
this latter troul)le as can readily l)e seen from Fig. 32. The 
American target fulfills tlie same reipiirements, but differs from the 
ordinary target in having two discs, one behind the otlier, as in 
Fig. 33. The principle of construction of this target is ex- 
tremely simple, and may be best explained in the figures above 
Supjiose a target of the old kind, which in its front view looks 
exactly like the front view of the new target in A, to be cut 
along the vertical lines an^ 1>1>, thus dividing it into three parts; 
that is, oub center-piece and two wings. Suppose furthermore, 
tlie center|)iece to remain in its former jilace at the front of the 
rod, while the two wings are removed to the rear of the rod. Then 
the result evidently will be that the horizontal line cr, di], will 
appear as one unbroken line to the observer, only when the rod is 
held jierfectly vertical. No deviation either towards the instru- 
ment, or away from it will cause the two jiarts cc and <hJ of the 
horizontal line situated at the rear of tlie rod in the wings of the 
target to show either above or below that ])art cd of the horizontal 
line which is situated in the front of the rod in the centerpiece of 
tlie target. 

"Whether using the bent target, the ordinary target or no 
target at all, it is apparent that the rodman should hold the rod in 
a Vertical ])osition, known as ])lunib. This can be done by stand- 
ing directly beliind the rod with both feet together or apart, as the 
rays of the sun may require, governing shadows, and holding the 
rod between the thumb and finger of one hand while moving the 
tari-et M'ith the other. After the target is set, both hands are 
brouidit in line with the shoulders, and standing erect, the hand 
should touch the rod very lightly, so that it will almost stand in a 
vertical position by itself; or when standing in that position if the 
center of the rod or the corner is made to coincide perpendicularly 



PLANE SUEVEYIIfG 39 

with the iiDse and chin, it w\\l he pluiiih. IThe rodiuaii should 
never |iut his hands aroi^nd the rod.j 

Another ■\vay is to sight along; the line of some huildino- 
apparently in line. There are, of course, many different methods 
of sitrualling, hut the ones mentioned are frequently used. 

"When the rod is to he read without the aid (.)f a tar^-et or with 
the ordinary target, it frequently happens that the rod is not ver- 
tical and the signal used for hringing it in its proper vertical 
plane is the raising of either the right or left hand in a vertical 
position, which indicates that the rod should he inclined in that 
direction. In so doing move the rod slowly until the hand is low- 
ered. After the target has heen set in its proper position, clamp it 
hy the screw on its side, then give another sight and note the sig- 
nals of the observer. 

If the target is to he moved, the observer should hold the palm 
of one hand in the direction the target is to be moved. The observer 
should \ise b\it one hand in sio-nalling the rod; if the target is to 
be lowered, he should hold his hand below his hip, palm down. 
To raise the target he should hold his hands above his shoulder, 
palm up. Any considerable change in the j^osition of the target 
is denoted by a more or less violent motion of the hand. If a very 
slioht change is desired, the observer should hold his hand in the 
projier position without moving it up or down. When the proper 
j)Osition of the target has been obtained, the observer indicates the 
fact by raising both arms above the head and moving them in the 
arc of a circle to indicate that the rod reading at that particular 
place is complete. 

New York Rod. This rod resembles the Philadelphia rod as 
to its use and dimensions, but ditfers as to scale and vernier read- 
ing. The scale is divided into feet, tenths and hundredths, the 
same as the Philadelphia rod, except the graduations of the hun- 
dredths, which instead of having the sides of one black space each 
equivalent to 0.01 foot, as on the Philadelphia rod, the hundredths 
are distinct by themselves, therefore, each line between the tenth 
is .01 part of the scale. Fig. 34 shows the rod at its full length, 
and Fig. 35 shows a sectional part thereof with its movable target 
set at (3-| feet and the black horizontal lines each indicate .01 as 
more fully explained hereafter. Fig. 36 shows the side with its 
graduations, as on the face of the rod and is set at 6^ feet. 



40 



PLANE SURVEYING 




e I'od Las a movable target wliicli carries a vernier, and 
•eadings to tliousaiidths. It cannot, however, be read with- 
out the aid of the target and is used for the most part, 
where precision is required; it probably commends its- 
self to a greater immbev of engineers, because of its 
stiffness and wearing qualities. For elevations up to 
C)i feet, the target is used in the same manner as the 
former I'od by sliding it up or down upon the rod. 
Above ('t\ feet, as with all the rods, the target is clamped 



& 



tfN 




^ 






«^ 



RED 



= 2 

-4 

= 6 

8 



91 



Fig. .34. 
at the (ii -foot division, 
half and when bo extended the vernier is on each of the narrow 
sides, im])resKed in the wood (See Fig. 30). It should be noted 
that while the vernier on the Philadel])hia rod i« situated ou the 



l-'ig. 35. Fig. 36. 

The back of the rod slides upon the front 



PLANE SURVEYING 41 

back when extended, with the New York rod it is on its narrow 
sides. The vernier in question is somewhat different from the 
one found on the Philadelphia rod, since it is provided with a 
direct vernier, while the other is provided with an indirect vernier. 
The former, as has been exjilained, is usually placed below the 
center of the tai-get. that is. the zero is placed below the in- 
tersection of the horizontal and vertical lines of the taroet. 
In almost every case this causes confusion because the rodnian 
has been taught, by reason of using a Philadelphia target rod, 
to read the scale at the zero of the vernier to tho fractional 
parts of a foot by looking along the vernier for tlie coincid- 
intr lines. There need be very little confusion in readino- the New 
York rod, if it is remembered that the center of the target is set 
by the k^veler and not the zero of the vernier as on the Philadel- 
phia rod. Carefnl observation of the vernier will show that the 
zero of the vernier is placed at the intersection of the horizontal 
and vertical lines of the target. The method of using the clamps, 
setting the target, etc., is the same as that of the Philadelphia rod. 

The Boston Rod is made of mahogany, is of the same length 
and slides out as the rods just described. It is distinctly a target 
rod and cannot be read without its aid. The scale and vernier, how- 
ever, are on the narrow sides and can be read to thousandths or 
any fractional part of a foot. The target is fixed upon one-half of 
the rod for elevations less than G-J feet. The target end is held ujjou 
the ground and the front of the rod slides upon the back, as shown 
in Fio-. 87. Above (>?, feet the rod is inverted as shown in Ficr. 
38, and is then used in much the same way as the New York rod. 
The figures above referred to show the sides of the rod with its scale 
upon it. The screws at each end act as clamps. In the old style of 
Boston rod a wooden target was screwed to the rod with the result 
that the target would warp and twist or be knocked off, thus render- 
ing the rod useless. The best type of Boston rod is fitted with a 
bent metal target. This form is very serviceable and satisfactory. 
It will be apparent from the foregoing description that the rod is 
read altogether by vernier, the scales and vernier being on the 
side. It is the lightest and neatest rod of the three but the least 
used. 

Cross=Section Rod. This is a rod 10 feet in length, painted 



42 



PLANE SUEYEYING 



white, with black irradiuitions; it is divided into feet, tenths and 
hundredths, (See Fi<r. 311). The scale is on both sides. At each 
end is a siiirit level bubble with graduations on the upper side of 
the tube to bring the rod in a horizontal plane. In the center of 
the rod is an opening for the hand, and thereby it can be easily 

taken from place to place. 
The purpose of this rod is to 
simplify the lengthy calculations 
in taking cross sections; this 
will be more fully explained 
under its respective head. 

In Fig. 39 A and B are the 
[bubbles. It is ajtparent that if 
' one end of the rod is jjlaced on 
the side of a hill and the other 
raised in a vertical position iintil 
the bubble appears in the center 
of the tube, the base of the rod 
will be in a horizontal plane. 

Ranging Poles. Fig. 40 
shows the three forms of ranof- 
ing poles (called flags) in com- 
mon use, all of which are from 
<) to 10 feet in length, made of 
hardwood, octagonal in shape; 
they are tapered from the top 
dowu and each foot painted al- 
ternately red and white, and pro- 
vided with steel shoes, except 
the smallest one, which consists of an iron tubular rod ^-inches in 
diameter and used for the most part on construction work. These 
flags are for the purpose of estal)lishing points or retaining a given 
line indeflnitely; it is an important tool of the surveyor's outrit. 
To use this flag, it is placed approximately at some reasonable 
distance from the instrument and then by the signals of the 
observer is moved until the line of sight through the instrument 
bisects it. It should be held in a vertical position and governed 
by the same methods used in placing a leveling rod in a vertical 




FiK. as. 



TLA^'E SrUVEYIXCI 



43 



position. It is also a conv^enieut device for measuring, approx- 
imately, distances not exceeding six feet, but where any great 
amoiint of accuracy is desired, the method should not be relied 
iipon. It is an advantage, however, to use the flag as a check, 



Fig. 39. 
vhen it may appear that some discrepancy has occurred. 

INSTRUMENTS. 
The Wye Level. There are tliree kinds of leveling iiistru- 
ments in common use, viz: The Wye level with four leveling 
screws, the AVye level with three levelincj screws and 
P Q a tiiQ Dumpy level. The AVye level derives its name 
from the vertical forked arms, called "^yes, in which 
the telescope rests. It is clamped to them by collars 
which may be raised allowing the telescope to be 
turned on its horizontal axis or lifted out entirely. 
It is also referred to as the four-screw level. Like 
other levels it is used for the purpose of ascertaining 
a horizontal line of sight parallel to a spirit level 
and perpendicular to the vertiqal axis. The line of 
sight is fixed in the telescope by the intersection of 
cross-hairs. A spirit level is attached to the under 
side of the telescope and is protected excejit on top 
by a metal tube. In the barrel of the telescope slide 
two tubes, in one of which is an eye-piece; in the 
other is the objective. 

The eije-jpiece usually found with the four-screw 
leveling insti'ument is of the erecting type. The in- 
verting eye-piece as distinguished from the erecting 
3 H H *?ye-piece has two lenses instead of four. The result 
is that the inverting eye-piece permits more light to 
reach the eye of the observer, and is therefore better 
adapted to precise leveling. At first some inconven- 
Fig. 40. ience is experienced by the fact that all objects arc 
iipside down, but a little experience will soon con- 
viuce the observer that all the advantages whether for a four- 



44 



PLANE SUEVEYIXG 



scroAV instrunu'iit or a tliree- screw instrument, lie with the 
invertinir eye-iiiec-e. Nearly all makers giv'ea purchaser his choice 
of the style of eye-piece without extra iharge. In purchasing an 




instrument it should be noticed whether the eye-piece is adjusted 
by a straight pull or by a spiral motion, because the spiral motion 
is usually considered more satisfactory. 



PLANE SrEYEYIXG 



45 




WYE LEVEL — THUEE SUKKW. 




Fig. 41. DUMPY LEVEL, 



40 



PLANE SlIEVEYING 




,''S ? 



s 



.^11 inexjjerifiiced observer upon looking through the level 
and liiuliiig no cross-liairs may suspect that the cross-hairs are 
broken. It must not be forgotten that the eye- 
piece must be focused before the cross-hairs will 
come into the range of vision. Ilavincr once 
focused the eye-piece upon the cross-hairs, the 
ad justment will stand for a long time if the eye- 
j)iece is undisturbed. 

The object glass is moved in and out Ijv means 
of a pinion which works on a rack attached to a 
slidincrtube and moves in the axis of the barrel, 
passing through the run which is inclined in 
the barrel. The instrument is provided with a 
clamp, slow motion and leveling screws and 
mounted on a tripod. The two former screws 
i5 are situated directly under the horizontal bar 
> and revolve with the telescope. 
_ The Line of Coliimation of a level is the line 
Y, joining the optical center of the object-glass 
2 iind the intersection of the cross-hairs, and since 
I this line determines the point towards which the 
P telescope is directed, it should coincide with the 
m optical axis of the telescope. The eye-piece 
^; and object-glass must be accui-ately centered. 
^^ Instrumental Parallax is an important con- 
^ (lition of focut^ing due to the fact that the image 
^ ^ doi's not fall in the plane of the cross-hairs. 
■55 To determine this, direct the telescope upon an 

object and focus the eye-piece so that the cross- 
hairs are perfectly distinct. Then turn the tele- 
scope upon the object which is to be observed, 
and focus the object glass until the image is 
clearly defined. Move the eye from side to side 
and note whether there is any apparent move- 
ment of the cross-hairs and image. If any is 
seen, the two operations are to be repeated until 
all parallax is removed. 
This adjustment depends upon the eye of the observer and 
when made for one person may not be correct for another. 



1 



"*i (3S3__r:i 3 



'^ E 



PLANE SURVEYING 47 

Spherical Aberration. This defect is caused liy combining 
lenses of diflferent curvatures so that objects on the side of a 
field of view are seen less distinctly than those in the center. To 
test the object glass for this defect cover the outer edge with an 
annular ring of paper and focus upon some desired object. Then 
remove the ring and cover the central spot of the ghifes; if no 
change of focus is needed the glass has no spherical aberration. 

To test the eye-piece, sight to a heavy black line drawn on 
white paper and held near the side of the field of view. If it aji- 
])ears perfectly straight the eye-glass is a good one. 

Chromatic Aberration is a defect caused by combining 
lenses of different and improper varieties of glass so that the yel- 
low or purple colors appear on the edge of the field. To test the 
telescope for this defect focus it upon a bright distant spot and 
slowly move the object glass out and in. If no colors are observ- 
ed around the edge of the field of view the telescope is free from 
this defect. 

Adjustments. The adjustments of the Wye-level are three 
in number and should be made in the following order: 

1. To make the line of collimation parallel to the bottoms 
of the collars. 

'2. To make the axis of the liubble tube parallel to the line 
of collimation. 

3. To make the axis of the bubble tul)e perpendicular to the 
vertical axis of the instrument. 

To make the test for the first adjustment set up the instru- 
ment firmly upon solid ground, shaded from sun and wind. Di- 
rect the telescope towards the side of a building, a fence or other 
convenient object and carefully center the intersection of the 
cross-hairs upon a well-defined point, such as the head of a tack. 
Clamp the vertical axis and loosen the telescope clips. Now 
slowly revolve the telescope in the wyes and note if the intersec- 
tion of the cross-hairs continues to cover the point. If so, the 
line of collimation is in adjustment. 

If the intersection of the cross-hairs moves off the point, re- 
volve the telescope in the wyes as nearly as possible through 180 
degrees and carefully center a point at the intersection of the 
cross-hairs in this last position. Bisect the distance between the 



48 PLANE SURVEYING 

two points and establish a third point; l)y means of the screws at- 
tached to the cross-hair diaphragm, move the diaphragm so that the 
intersection of the cross-hairs covers the third point. Now re- 
peat the test and correct the position of the cross-hair diaphragm 
until the intersection of the cross-hairs covers one point as the 
telescope is revolved in the wyes. 

The horizontal cross-hair should at all points be at the same 
distance from the bottoms of the collars. To test this, carefully 
center one extremity of the hair upon a point, and by means of 
the tangent screw, slowly revolve the telescope upon the vertical 
axis, and if the hair covers the point from end to end, the adjust- 
ment is complete. If it does not, the hair is to be adjusted by 
the same screws as before. Making this adjustment will probably 
disturb the former one, and the two are to be repeated in succes- 
sion until satisfactory. 

It will be noticed that to nuike this adjustment, it is not nec- 
essary to level the instrument. 

Adjustment of the Axis of the Bubble=tube. To test this 
adjustment, iirst throw back the clips holding the telescope in the 
wyes, and then revolve the telescope upon the vertical axis 
to liriniT it directly over a pair of leveling screws and clamp the 
axis tirmly. By nu'ans of these leveling screws bring the biihl)lc 
to the center of the tul)6 as accurately as possible. Now without 
disturl)in<>' the instrument, carefully lift the telescope out of the 
wyes and turn it end for end, being careful when replaced in the 
wyes that the telescope comes to its seat at each end. If the bub- 
ble in this new position of the telescope comes to rest at the cen- 
ter of the tube, tiie axis of the tube is in adjustment. 

If the Imbble does not return to the center, bring it one-half 
way back to the center by means of the vertical screws at one end 
of the bubble-tube, and the remainder of the way by the two lev- 
elincr screws. Now repeat the test and correction as often as nec- 
essary until the bubble remains in the center of the tube. 

Ilavino- adjusted the bubble-tube over one pair of screws, 
test it over he other pair. 

When the horizontal hair is truly horizontal, the line of colli- 
mation and the axis of the bubble-tulje should be in the same 
vertical plane. To test this, after tlie previous adjustment has 



PLANE SURVEYING 49 



been completed, loosen the clips of the wyes and bring the !)ub1)le 
Ciirefully to the center of the tul)e. Now slowly revolve the tele- 
scope in the wyes and note if the bubble still remains in the cen- 
ter of the tube. If it does, the line of colliniation and the axis of 
the tube are in the same plane. If the bubble runs to one end of 
the aibe, bring it i)aek by the horizontal screws attached to one 
end of the tube. 

It must be borne in mind that the first and second adjust- 
ments must be carefully made and that they are absolutely essen- 
tial if satisfactory results are to be attained \vith the instrument. 

Adjustment of the Vertical Axis. This adjustment is not 
absolutely essential, provided that every time a reading is taken 
the bubble is brought to the center of the tube by means of the 
parallel plate screws. However, the adjustment will expedite 
field work and should always be made. 

To test, level the instrument carefully over l)Otli jiairs of 
screws; if the bubble remains in the center of the tube as the tele- 
scoj)e is revolved on the vertical axis all the way round, the ad- 
justment is complete. If the bubble runs to one end as the tele- 
scope is thus revolved, the vertical axis is out of adjustment aiuC 
may be connected as follows. Bring the telesco])e directly over a 
pair of opposite plate screws, and by means of these screws l)i'ing 
the bubble accurately to the centei- of the tube. Now re\olve tlic 
telescope on the vertical axis as nearly as jiossible through 1>H) 
degrees anil note the displacement of the bubble: bring the bub- 
ble one-half of the way back to the center by the screws, at one 
end of the bubble-bar attached to the wyes, and the remainder of 
the distance by the parallel plate screws. Repeat the test and 
adjustment until the bubl)le remains in the center of the tube in 
all positions of the telesco]>e. 

Replacing the Cross=hairs. The cross-fiairs in leveling in- 
struments may be either spider webs or platinum wire. Spider 
webs are better, but in selectino- them care should be taken to see 
that they are free from dust and dampness. Probably the web of 
the little black spider is the most satisfactory, but the web of the 
common spider will give good i-esults, especially if freshly 



50 PLANE SUR\T:YING 

spiin. Spider webs can best be carried Ijy wiuding them 
around a stick. 

The cross-hairs are attached to the small diaphragm set at 
the principal focus of the object-glass. To replace the cross-hairs, 
carefully remove the diaphragm from the telescope tube and lay 
it upon a white surface with the cross-hair side upwards. It will 
be noticed that there are incisions upon the face of the diaphragm 
intended to indicate the position of the cross-hairs. Fasten one 
end of the spider web to the diaphragm by means of beeswax or 
paraffine, carefully suspending the other end of the web over the 
opposite incision upon the diaphragm; after the web has been 
properly stretched by fastening it to a match, fasten the web 
down as before. Repeat the operation with the other cross-hair, 
then replace the diaj)hragm in the instrument, care being taken 
not to break tiie hairs. Tiie first adjustment may then be made. 

The Dumpy=level. This instrument (see Fig. 41) difPers 
from the Wye-level in the following points: the uprights which 
carry the telescope are firmly attached to the bar. and the line- 
tube is mounted on top of the bar. The telescope is attached 
firmly to the uprights so that the whole structure is rigid. At- 
tached to one of the uprights is a projecting piece with which one 
end of the level is connected in such a way as to permit of a 
slight horizontal movement. The other end of the level-tube is 
fixed with two capstan-headed nuts to permit of vertical adjust- 
ment. 

A clamp and slow-motion screw should be attached to the 
center. This, while not an absolute necessity, will, when clamped, 
prevent unnecessary wear on the center when the instrument is 
carried upon the shoulder. The telescope may be either erecting 
or inverting, but the latter is to be pivfened. 

The dumpy-level, though not as convenient in its adjust- 
ments as the "Wye-level, will, nevertheless, when properly adjust- 
ed, give equally good results; while on account of its simplicity and 
compactness, it is not so liable to have its adjustments disturbed. 

Adjustments. The adjustments of the dumpy-leve! are two 
in number and should be made in the followingr order: 

1. To make the axis of the bubble-tube perpendicular to the 
vertical axis of the instrument. 



PLANE SURVEYING 



51 



2. To make the line of collimatiou perpendicular to the 
vertical axis of the instrument. 

To make the first adjustment, set up the instimment firmly 
in a position shaded from sun and wind. Turn the telescope over 
a pair of opposite plate screws, and by means of these screws 
hringthe bubble accurately to the center of the tube. Repeat the 
operation over the other pair of screws, and so on alternately over 
each pair of screws, until the bubble remains as nearly as possible 
in the center of the tube for both positions of the telescope, care 
being taken not to swing the telescope through more than 90 de- 
grees. 

Now turn the telescope accurately over a pair of opposite 
plate screws and after leveling carefully, swing the telescope 
through 180 degrees directly over the same pair of screws. If the 
bulible remains in the center of the tube, the adjustment is com- 




Fig. 43. 

iilete. If the bul^ble does not remain in the center of the tube, 

bring it one-half way back to the center by means of the vertical 

capstan -headed screws at one end of the tube, and the remainder 

of the distance by the leveling screws. Now repeat the test and 

adjustment until the bubble remains in the center of the tube 

through all positions of the telescope. 

The second adjustment of the dumpy-level must be made by 

the "Peg Method". Select a piece of ground as nearly level as 

jTOssible and lay out a straight line upon it, from 400 to 600 feet 

in length, drivino- a stake at each end and at the center. Set up 

the level over the center stake and after leveling carefully direct 

the telescope to the rod held upon N (see Fig. 43), and take the 

reading by the target. Now direct the telescope to the rod held 

at M and take the reading. The difference of these two rod read- 
er 

ings at N and M will join the two differences of elevations, no 
matter how much the line of collimation is out of adjustment. 



52 PLANE SURVEYING 

Now set up the instniinent witliiii about twenty feet of the 
stakes, as N, and take the roil reading; carry the rod to M and 
take the readincp. If the difference of these last two readings is 
the same as before, the line of coUiination is in adjustment; if not, 
correct nearly the \¥hole error by means of the upper and lower 
capstan -lieaded screws attached to the diaphragm carrying the 
cross-hairs. Repeat the test and correction several times until the 
difference of elevation from l)oth positions of the instrument agree. 

It may l)e well to note right here that the second adjustment 
of the Wye-level may be made by the " Peg Method," but it is 
thought that the method given is tlie more convenient. 

The Precise Spirit Level. The description of this instrument 
which is shown in Fiij. -44 is taken from the catalogue of the 
makers, F. E. Brandis, Sons, & Co. 

The princij)le underlying the construction of the instrument 
is that the telescope can be moved in a vertical plane about a hor- 
izontal axis by means of a micrometer screw. Tiiis construction is 
especially adapted to the object in view, viz: of multiplying the 
pointings on a mark either in the horizon of the instrument or at 
an angle above or below. 

The superstructure consists of two u])rights joined somewhat 
below their Jiiiddle by a horizontal plate. Tlie upper portions of 
theu[)rights are fashioned into Y's, and carry the telescope and the 
striding level; the lower portions are cut out so as to leave guide 
pieces passing outside the lower plate. A capstan-headed pivot 
screw passes througli each guide piece at one end into small sock- 
ets in the fixed plate. Passing through the fixed plate, the mi- 
crometer screw moves Itetween the guide pieces at the other end 
and al)Uts against a small steel surface. Thj fixed plate carries an 
index, and one of tiie guide pieces a corresponding scale to register 
the whole terms of the micrometer, and also a pointer for reading 
the subdivisions of the micrometer head of which there are 100. 

The Gurley Binocular. The binocular hand level, as the 
word implies, is a hand level with a double telescope attached. It 
vs similar to the monocular hand level in many respects, except it 
is provided with screw centering and focusing adjustment and 
can be adjusted to the different widths of the eye, avoiding all 
strain to tlie ocular muscles. 



PLANE SURVEYING 



53 



Adjustment. Follow the ])riiK'iples as laid ilown coiiferning 
the Locke hand level. 

The Qurley Monocular Hand Level. This iiistriiiiieut is a 
telescope hand level, by wliich readings are more definitely deter- 
mined on a rod at some distance than is possible with the ordinary 
hand level. 




Adjustment. Follow the principles 'as laid down relative to 
the Locke hand level. 

" Setting up " the Instrument. The term " setting up the 
level" means to place it in'position to secure horizontal sights. To 
do this, plant the legs firmly in the ground at approximately 



54 



PLANE SURVEYING 



equal distances apart so as to make the leveling plate horizontal. 
Bring the telescope directly over and in line with the two leveling 
screws between the plates and opposite each other. As you stand 
facing the instrument turn the thumb of the left hand in the di- 
rection of the motion of the bubble and turn both thumb screws 
towards or away from each other, being careful not to strain the 
level plates by having the leveling screws too tight. These screws 
should bear firmly upon the ])lates and should move 
witii ease and smoothness, but there should be no movement 





Fig. 4.-,. Fig. 4*5. 

of thf vertioul axis of the instrument. Turn the screws 
until tile 1(ul)ble aj)j)ears along the graduations of the bub- 
l)lf tube and bring it to the middle, then turn the telescope at 
ri<dit aiKfles to these two screws and over the other two. In like 
manner perf(jrm the same o|)eration as before. This will cause the 
bul)ble to run away from its former position; l)ring the bubl)le ac- 
curately in the center of the tube over these screws, that is, hav- 
ing ecpial spaces on each side of the zero of the scale, then turn 
the telescoj)e over the former screws and bring the bubble in the 
center. Do this several times until the biibl)le remains stationary 
at any angle the telescope may turn; to test this, turn the telescope 
Lalf way around and see if the bubble moves; should it remain 
stationary, the instrument is level. The level is, with few e.xcep- 
tions, never placed in line (except when being adjusted under the 



PLANE SURVEYING 55 

peg method). It is usually placed iu some convenient spot where 
the greatest number of horizontal sights can be secured. As al- 
ready stated, the tripod legs must be so placed as to make the 
plates horizontal. This will save time iu bringing the bubble in 
its proper position. Should it be required to set uj) the instru- 
ment on the side of a hill, place one leg at an altitude and the other 
two in apparent line with each other ( see Figs. 45 and 46 ), 
but where the tripod is adjustable the proper method is apparent. 

After the instrument is set up and leveled, focus the eye- 
piece upon the wires and focus the object-glass on the rod by 
means of the screw placed for that purpose on the top or side of 
the telescope Care should be taken not to take a reading until 
the bubble has been carefully observed and brought in the exact 
center of the bubble tube. When this is completed, sight throui'h 
the telescope and note the rod reading or set the target rod; again 
look at the bubble and see if it has moved away from its former 
position; if not, again sight on the rod and see if the first observa- 
tion was correct. Should the intersection of the cross-hairs fail 
to coincide with the horizontal and vertical lines of the target or 
the center of the rod. the rodman is to incline the rod by the sig- 
nals of the observer, until it coincides or is in line of coUimation. 

Care of the Instrument. This duty pi-operly belongs to the 
instrument man or leveler, and the requirements should be thor- 
oughly understood. While in the field, the instrument remains 
on the tripod and is carried from place to place as the work re- 
quires, but when taken any distance, such as on railway trains, 
street cars, etc., it should be carefully placed in the box and car- 
ried by one who is capable of giving it proper care and attention. 

The instrument man being responsible for the instrument, it 
is natural, and perhaps best, that he should always carry the in- 
strument. In fact, the greatest amount of precaution should be 
exercised in the care of the instrument, both in the field and while 
conveying it. 

Instruments in general, the level in particular, should never 
be unduly exposed to the rays of the sun, as this will have a tend- 
ency to throw its various sensitive parts out of adjustment, there- 
fore, whenever possible, place the instrument, whether it is on the 
tripod or not, in the shade. 



56 PLANE SURVEYING 

The leveler should always exercise great care not to disturb 
the instrument after it is set up and should avoid, as much as 
possible, walking around it unreasonably, especially if the ground 
is soft, or the fiosition of the instrument not very firm. This ap- 
plies to all persons whether in the active performance of duty or 
not. It is frequently necessary to set up the instrument in places 
such as loose timber, rocks, etc., thus the importance of this care is 
apparent. If disturbed to any great extent it will be necessary to 
relevel it, and if the position of the legs of the tripod is disturbed, 
the entire work must be done over, because the height of the instru- 
ment will not be the same as in its former position. Should the in- 
strument be disturbed after a turning point has been established 
and its elevation ascertained, it will only be necessary to take a 
reading on the last turning point to determine the new height of 
the instrument. After leveling, the instrument man should keep 
his hands off the instrument except for the purpose of leveling and 
adjusting the telescope. He should not luake a practice of leaning 
his weight on the tripod. It is often necessary to send instruments 
great distances, and in so doing, in no case should it be sent by 
express or freight without first being pro])erly packed and secured 
against breakage; because of its fine construction and sensitive- 
ness it may get out of adjustment to such an extent as to render 
it impossiljle to readjust it for good work by any method known- 
to the engineer, and may become worthless and beyond repair even 
to an instrument maker. 

The student should appreciate that the care of the instrument 
is just as important to good work as its original excellence. 

Leveling. To determine the difference in elevation between 
two points, both of which are visible from a single position of the 
instrument, set up the instrument in such a position that the rod 
held upon either point will be visible. Now send the rod to one 
of the points as at A in Fig. -IS; direct the telescope upon it and 
take the rod reading; now direct the telescope to the rod held at 
B and again note the reading. Evidently the difference of the rod 
will give the difference in elevation of the two points. 

If the points are too far apart or if the difference of elevation 
is too great to be determined from one setting of the instrument, 
intermediate points must be taken. For instance, suppose it is 



PLANE SURA'EYING 



57 



desired to find the difference of elevation of A and C in Fig 47, 
C being too far below A to permit of being read upon both points 
from a single position of the instrument. Set wp the instrument 
(not necessarily on line from Ji. to C) in some position such that 
the line of sight will strike the rod as near its foot as it is pos- 
sible to take a reading: send the rod to some point I! such that 
the line of sight will strike the rod near the top when extended. 
The difference of these rod readings will give the difference of 
level of A and B. Now carry the instrument to some point such 
that rod readings can be taken upon B and 0. The difference of 
the rod readings upon B and C added to the difference of rod read- 




Pig. 47. 

ings upon A and B will give the difference of level of A and V. 
proper attention being given to signs. 

If the line of levels is very extended the abov^e method is 
awkward, as some of the differences will be positive and 
some negative. Choose some plane called a datum plane, such 
that all of the points in the line of levels will lie above it. 

Begiiming at the point A, assume the elevation of the point 
above the datum plane. Read the rod held upon A, and the read- 
ing added to the assumed elevation will give the height of the 
cross-hairs above the datum plane, called the "height of instru- 
ment" (ILL). Now, turn the instrument upon the point B and 
read the rod and it is evident that this last rod reading subtracted 
from the height of instrument will give the elevation of B above 
the datum plane. Next move the instrument beyond B, or at 
least where it can command a view of B and C and again sight to 
the rod held upon B. This last rod reading added to the elevation 
of B will give the new height of instrument from which if the rod 



58 



PLANE SURVEYING 



reading at C is subtracted will give the elevation of C above the 
datum plane. Fig. 48 vpill make the method of procedure apparent. 
Referring now to that figure, the first rod reading taken upon 
the point A is ordinarily called a '"back-sight" and the first read- 
ing taken upon B is called a '-fore-sight". There seems to be no 
good reason for adhering to this method of distinguishing between 
the rod readings and it is illogical and misleading. A back sight 
is not necessarily taken behind tlie instrument, that is, in a direc- 
tion contrary to the progress of the survey, neither is a fore-sight 




FiK. AS. 



necessarily taken in front of the instrument. It is more logical 
and less misleading to designate these rod readings by the terms 
"plus-sight" and "minus-sight". 

A plus-sight, tlun-efore, is one taken upon a point of known 
or assumed elevation, to determine the height of instrument. 

,V minus-sight isone taken upon a jioint of unknown elevation 
and which, subtracted from the height of instrument, will give the 
required elevation. 

A ''Ijench-mark" (B.M.) is some ol)ject of a permanent 
character, the elevation of which, together with its location, is 
accurately determined for future reference and for checking the 
levels. 

A '"peg", '"plug", or turning point" (^T.P.), is a ])oiiit used 
for the purjiose of ciianging tlie position of the instrument. This 



PLANE SURVEYING 59 



tiirnintT point may be taken upon a beneh-mark. bnt is oftener 
taken upon the top of a spike or stake driven into the ground. 

If a self-reading rod is used, the instrument man will carry 
the notebook and record the rod readings as they are observed. 
The leveler should cultivate the practice of calculating the ele- 
vations of his stations as the work progresses, thereby enabling him 
to discern errors when they occur. 

If a target rod is used upon the work, the rodman should also 
carry a notebook in which he should at least enter all readings 
upon turning points and bencli-marks and check up with the in- 
strument man at every opportunity. Under the circumstances, 
the instrument man is more or less dependent upon his rodman 
for the correct reading of the rod and when an inexperienced rod- 
man must be employed, the self -reading rod will give the better 
results. 

The limit of range of an ordinarv levelinginstmiment is about 
■400 feet, and sights should not be taken at a greater distance. 

The method of keeping the field notes for the work above out- 
lined is given below. A level notebook especially adapted to 
the purpose should be procured, the notes entered on the left-hand 
pages, the right-hand pages being reserved for remarks, sketches, 
etc. 



St A. 


+ s 


ILL 


— s 


Elev. 




A 


O.G.jO 


lOOO.OuO 




1000.00 


© N. E. cor. 


B 


1.250 


9113.1-10 


8.700 


991.890 


of abutment 


(! 


2.380 


987.070 


7.850 


985.290 


Main street 


D 






9.570 


978.100 


bridge. 



It will l»e noticed that the algebraic sum of the plus and 
minus readings eqirals the difference of elevation of the first and 
last stations, and these quantities should be checked as often as 
possible to discover errors in addition or subtraction. 

Profile Leveling. The method of profile leveling is the same 
in principle as above outlined, but the details of field work are a 
little different. 

In this sort of work it is intended to determine a vertical 
section of the ground above a datum plane. To this end, rod read- 
ings are taken sufficiently close together that when the elevations 



60 



PLANE SURVEYING 



are i)lotted aiul the points connected, tlie resultino- irreo-ular line 
will closely approximate the actual line of the surface. 

Profile levels are usually run in connection with a transit or 
ch;un survey of the line, the positions of the points being first 
established upon railroad surveys. These points are usually 100 
feet apart unless the ground is very irregular, when they may be 
50 or 25 feet apart or even less, the points being indicated by 
stakes. Upon sewer or street work they should seldom be more 
than 50 feet apart and the readings should be taken with the rod 
held upon the ground. 

Fig. 49 will illustrate the difference between profile leveling 
and tlu' first system outlined, sometimes called differential leveling 
or "])eg''' leveling. Ileferring now to that figure' A B is the datum 




Fig. iO. 

plane and the full lines at C,D, and E represent positions of the 
rod for turning jtoints. Assuming the elevation of the point C, 
the rod is lield upon it and the reading added to the elevation for 
the height of instrument. The rod is then carried successively to 
the points a, h, r, >/, and each reading is in turn subtracted from 
the height of instrument <at C, to get the elevations of these points. 

The rod is tiien held upon the point D, the instrument moved 
and the plus-sight upon D added to the elevation for the new 
height of instrument. The rod readings upon c, /", (/, //, /, etc., 
are then each sul)tracted from this new height of instrument for 
elevations. 

This figure illustrates the improper use of tb" terms back- 
sight and fore-sigiit. The rod readings at C, a, and /> are taken 



PLANK SURVEYING 



61 



behind the iiistnimeiit, but the rod readino; at G is tlie only 
plus-sight. 

The method of keeping the tield notes is illustrated below. 



Sta. 



O. 

+ 50 
1 

+ 50 
T. P. + G2 
2 

~ + 50 
3 

4- 50 
4 



+ S 
3.25 



2.04 



II. I. 


— S 


Elev. 


585.70 




582.45 




3.7S 


581.92 




4.18 


581.52 




5.06 


580.64 


5S1.40 


6.85 


578.85 




3.10 


578.39 




3.18 


578.31 




3.90 


57.7.59 




4.60 


576.89 




5.25 


576.24 



CR0SS=SECTI0N1NG. 

One of the most imjioi'tant prol)lems tliat confronts the 
leveler is the setting of "slope stakes," called cross-sectioning, 
from which may be determined the amount of earthwork in cut 
or till, and which mark the extreme limits of the operations of the 
construction corps in building railways, highways, sewers, canals, 
irrigation ditches, etc. 

The problem is as follows: Given, the required width of 
finished roadbed or channel, with proper side slopes (depending 



vyiktW^'^^/.'/.ywmmf^'^''^^''^''^^^^^ 




20' 

FiK. 50. 



upon the kind of material), it is required to determine where 
these side slopes will intersect the natural surface of the ground 
with reference to the center line of the survey. The center line is 
defined by stake, carefully aligned and leveled, and a profile of it 
is prepared upon which the grade line is laid down, showing the 



62 



PLANE SURVEYING 



elevation of the tinished roadbed or channel with reference to the 
natural surface of the ground. 

Let us assume the ground to be level transverse to the center 
line. Depth of cut at center = 12 feet; side slopes 1^ feet hori- 
zontal to 1 foot vertical ; width of cut at bottom = 20 feet. See 
Fig. 50. 

Set lip the instrument in some convenient position that will 
command a view of as much ground as possible. Hold the rod 
upon the ground at the center stake and note the reading. Sup- 
pose it to be 3.5 feet. Now if the ground is level, the distance 
from C to B is evidently 10 + (12xlA) =28 feet and the rod 
should acrain read 3.5 feet when held at B. The point A would 
be found in the same way. 

Tlie notes would be kept as shown below. 



Sta. 


Dis. 


Left 


1 Center 


E 


ight 


Area 


C.Tds. 


175 


50 


+ 12.0 

28 


+ 12.0 




+ 12.0 

28 






17(5 




+ 3.0 
14.5 


+ 6.0 


+ 7 
9 


+ 9.2 
23.80 






170 


50 


+ 2.5 
13.75 


+ 5.0 


+ 8.0 
22 







The preceding example illustrates one of the simplest cases 
tiiat occur in jiractice. Let us now take the case of a line located 
upon the side of a hill. See Fig. 51. 

Depth to grade at center 6 feet; width at bottom 20 feet; 
side slopes 1^ to 1. As before, hold the rod upon the ground at 
C and determine the height of instrument above 0. Suppose this 
to be 5.5 feet. Now, if the ground were level through C it would 
l)e necessary to measure to the right 10 + (OxlA) — 19 feet to the 
point D and the rod should read 5.5 feet. Instead it reads, say 
2.8 feet. We know therefore that we have not gone out far 
enough by (5.5 — 2.8) 14=^4.05 feet, if the ground were level 
through the point D, bringing us to the point E where the rod 
should read 2.8 feet. Suppose it reads 2.3 feet. We must then 
go out 0.75 foot farther, each move bringing us closer and^-closer 
to the point B. This operation niay be repeated as often as is 
considered necessary, but with a little experience iu this sort of 



PLANE SURVEYING 



63 



work the instrument man can direct the rod closely enough to the 
point B for all practical purposes. We then enter the notes in 
the second line of the record shown above. 

Upon the left of the center, these operations are reversed. 
That is to say, we measure out 19 feet and instead of the rod read- 
ing 5.5 feet, it reads, say, 8.5 feet. AVe know then that we are 
out too far by 4.5 feet. We then nu)ve in toward the center the 




Fig. 51. 
reipiired distance and read the rod again, noting how much it dif- 
fers from N.5 feet, if any, and enter the final results in the notes. 

A third case is shown in Fig. 52, iu which the transverse 
slope is not uniform. The method of procedure is the same as in 
the other cases, but the rod should be held at the point where the 
slope changes in order to find its height above grade. Enter this 
and the distance out in the third line of the notes. 

The transverse section may be very irregular, in which case 
it may be necessary to take readings at several points in order to 




Fig. .52. 
calculate the area of the sections with more exactness. At times 
a section will be cut partly in rock and partly in earth, forming a 



64 



PLANE SURVEYING 



compound section. Each material will, of course, have its own 
proper side slope, and the depth and extent of each must be deter- 
mined hy soundings. 

In case the section is in fill instead of in cut. the method is 
the same as in the preceding cases, as will be illustrated in the fol- 
lowing examples. Let us first take a section level transversely. 

See Fig. 53. 

In this case the finished grade is to be U feet above the point 



9' 



Fig. .5.3. 
I'. Hold the rod at C and suppose it reads 3.25 feet. ]S'ow since 
the ground is level we go out to the right and left 9+(9xli) 
= 22.5 feet and set the stakes at A and B entering the record in 
the notebook as before, except that now the numerator of the 
fraction will be marked — instead of +. 

We will next take the case where the surface of the ground 
has a transverse slope. See Fig. 54. Kow hold the rod at the 
point C, and suppose it reads 9.25 feet. ]S'ow if the ground were 




Fig. .54. 
level through C we would have to go out to the right 9 + (0.2o 
X 1.5) = 18.4 feet to some point D. But there the rod reads, say, 
1.5 feet, hence we know we are out too far by ~.~5X 1-5 = 11. G3 
feet, bringing us back to some point as E and the rod now reads, 



PLANE SURVEYING 65 

say, 3.5 feet aud we move out again 2.0 X 1.5 = 3 feet. Therefore 
we move back and forth until we find the point B where the com- 
puted rod reading and the actual reading agree. 

Sometimes it will be found that a part of the section is in 
ci;t and a part in till, but liiethods outlined will serve in any case. 

The distance between the sections longitudinally will depend 
upon the nature of the ground. On uniformly sloping or level 
ground they may be taken 1(10 feet apart. Over uneven ground 
it may be necessary to take them as closely together as 25 feet or 
even less. In the sections themselves, a sufficient number of rod 
readings should be taken that the area of the sections may be 
determined with reasonable accuracy. 

After the field work is completed, the notes are plotted, 
usually upon ci-oss-section j)aper, and the areas determined either 
with a planimeter, by Simpson's rule or some other method. These 
sections then divide the earthwork into a system of prismoids of 
which the volume must be calculated. The formula for calculat- 
ing volumes is known as the Prisjuoidal Formula and is as follows: 

~ (A + 4M-fB) 

6X27 ^ ' 

in which / = length between consecutive sections, A ;= one end sec- 
tion, B = the other end section and M ^ the section midway be- 
tween the two. The result is given in cubic yards. 

The mistake must not be made of assuming that M is a mean 
between A and B; but a theoretical section must be plotted whose 
dimensions are a mean between those of A and B. This often 
results in quite a comjjlicated problem, and various other formulas 
have been devised to give sufficiently close results without the 
labor and time involved in the preceding. This will be treated in 
detail in Ilailroad Engineering. 




a -a 

'"So? 

* 0/ o 



H t"- t 












PLANE SURVEYING. 

PART II. 



The meridian plane of any place uxjou the earth's surface 
is a great circle passing through the zenitli of the x^lace and the 
poles of the earth. A true meridian is, therefore, a line lying in 
this plane, and would, if produced, pass through the poles. 

The magnetic meridian plane woTild iu the same way be 
detined by the zenith and the magnetic pole of the earth ; but since 
this pole is not fixed in position, the magnetic meridian is defined 
as the direction of the line indicated by the position of the 
magnetic needle. 

At a few i^laces iipou the surface of the earth, the true meridian 
and the magnetic meridian coincide at times, but for the most 
part they differ in direction by an ever varying quantity. The 
angle at any place between the true meridian and the meridian as 
defined by the magnetic needle, is called the magnetic declination 
for that place. If the direction of the magnetic meridian were 
constant, or if the changes followed any particiilar law, it would 
be a comparatively simple matter to determine the declination for 
any time or place. The variations occurring are of tliree principal 
kinds — diurnal, anni;al, and secular, the last being the most 
important. 

Diurnal Variation. On continuing observations of the 
direction of the needle throughoiit the day, it will be found that 
the north end of the needle will move in one direction from about 
8 A. M. rmtil shortly after noon, and then gradiially return to its 
former iDosition. 

Annual Variation. If observations be continued throughout 
the year, it will be found that the diurnal changes vary with the 
seasons, being greater in summer than in winter. 

Secular Variation. If accurate observations' on the declination 
of the needle, in the same place, are continued over a number of 
years, it will be found that there is a continual and comp)aratively 
constant increase or decrease of the declination, continuing in the 
same direction over a long period of years. 



70 PLANE SUKVEYING 

Besides the above, the declination is subject to variations more 
or less irregular, due to local conditions, lunar pertiirbations, sun 
spots, magnetic storms, etc. 

The declination in any part of the United States may be 
approximately determined by consulting the chart issued from time 
to time by the United States Coast and Geodetic Siirvey. (See 
chart, page 132.) Upon this chart all points at whicli the needle 
jjoints to the tn:e north are connected by lines, called lines of no 
declination. Lines are also drawn connecting points of tlie same 
declination, called isogonic lines. 

The isogonic curves or lines of ciiual magnetic declination (variation 
of compass) are drawn for each degree, a + sign indicating West declination, 
a — sign indicating East declination. 

The magnetic needle will point due North at all places through which 
the agonic or zero line pa.sses, as indicated on the chart. 

Before undertaking an extensive or important survey, it is 
the first duty of the surveyor to determine accurately his declina- 
tion. This is best done by laying out a true meridian upon the 
ground and comx^aring its direction with that indicated by the 
needle. Before describing the metliods of laj'ing out a true 
meridian, it will bt^ best to describe the cguipass. 

THE COMPASS. 

Construction. The surveyor's comjmss consists ijrimarily of 
a circular brass box, carrying, ux)on a pivot in its center, a strongly 
magnetized needle (see Fig. 56). The inside edge of the box on a 
level with the needle, is usually graduated to half degrees, and 
smaller intervals may be " estimated." Two jDoints diametrically 
opix)site each other are marked 0°, and form the north and south 
ends of the box, the south end being indicated by the letter S, and 
the north end either by the letter N or by a fleur-de-lis or other 
striking figure. The divisions extend through 90° upon both sides 
of these points, to the east and west points marked respectively 
E and W. The east side of the box, however, is on the left as the 
observer faces the north end; this is because the needle remains 
stationary while the box revolves around it. The divided circle is 
sometimes movable, being fitted with a clamp and tangent-screw 
for setting off the declination of the needle. 



PLANE SURVEYING 



71 



The magnetic needle is the most essential part of the compass. 
It consists of a slender bar of steel, nsnally five or six inches long, 
strongly magnetized, and balanced on a pivot so that it may turn 
freely and thus continue to point in the same direction however 
much the box carrying the pivot may be turned aromid. To this 
end the pivot should be of the hardest steel, ground to a very 
fine point, or, better still, of iridium; and the center of the needle 
resting upon the pivot should be fitted with a cap of agate or other 
hard siibstance. 

To distinguish the ends of the needle, the north end is usually 




Fig. 50. 

cut into a more ornamental form than the south end, or the latter 
end may be recognized by its carrying a coil of wire to balance the 
"dip." 

Intensity of directive force and sensitiveness are the chief 
requisites in a magnetic needle, and nothing is gained by making 
a needle over five inches in length. Indeed, longer needles are 
liable to have their magnetic properties im^^aired by polarization. 
The needle should not come to rest too quickly. Its sensitiveness 
is indicated by the number of vibrations that it makes in a small 
space before coming to rest. Should it come to rest quickly or be 
sluggish in movement, it indicates either that the magnetization 



72 



PLANE SUKVEYING 



is weak or that there is iiiidue frictiou between needle and x^ivot. 
The mider side of the box should be fitted with a screw which, 
engaging a lever upon the inside of the box, will serve to lift the 
needle off the pivot when the instrument is carried about. 

The sights form the next most important feature of the 
compass. They consist of two brass ii^jrights, with a narrow slit 
in each, terniiuated at intervals by circiilar apertures. They are 
mounted directly upon the compass-box; or the bottom of the box 
may be extended at eacli end in the form of a plate, ;ind the siglits 
attached at the ends of the plates. How- 
ever mounted, the sights should have 
their slits in line directlj^ over the north 
and south points of the divided circle. 
The right and left edges, respectively, of 
the sights, may have an eye-jiiece and a 
series of graduations, by which angles 
of elevation and depression for a range 
of about twenty degrees each way can 
taken with considerable accuracy. 
This device is called a tangent scale, 
tlie graduated edges of the nortli siglit 
being tangents to segments of circles 
having their centers at the eye-pieces, 
Pig. 57. and their points of contact with the 

tangent lines at the zero graduations of the scale (see Fig. 50). 
The spirit levels may be placed at right angles to each oth(>r 
in the bottom of the compass-box, or mounted in the same way 
upon tliG plate. 

The compass is usually fitted to a sijindle made slightly 
conical, which has on its lower end a ball turned perfectly spherical, 
confined in a socket by a pressure so light that the ball can be 
moved in any direction in leveling the instrument. The ball is 
placed eitlier in the brass head of a Jacob staff, or, better, in the 
top casting of a tripod. 

A plumb-bob should be provided with the instrument to center 
it over a stake. 

A telescope is sometimes X3rovide(l, to be attached to one of 
the vertical sights, for tlie purjijose of more clearly defining the 




PLANE SURVEYING 73 

line of sight. The compass is, however, so inaccurate that it wonld 
seem to be an lumecessary refinement. 

Prismatic Compass. This is a form of compass nsed in 
general where merely ordinary work is required. It is abotit 
3 inches in diameter with a floating metal dial (see Fig. 57), and is 
provided with folding sights and prism. By means of the latter it 
may be read while being pointed. This is especially useful when 
the instrument is held in the hand. Although it can be mounted 
on a Jacob staif, it is usually held in the hand and carried in the 
observer's i^ocket. 

Adjustment. To Adjust the Levels. First bring the bubbles 
to the middle of the tube bj- the pressure of the hand on diti'erent 
parts of the plate, and then tiiru the instrument half-way round. 
If the bubbles remain in the middle of the tubes, the tubes are in 
adjustment. If the bubbles do not remain in the middle, raise 
or lower one end of the tube to correct one-half the error. Relevel 
the instrument, again test, and apply the correction as before. 
Continue the ox3eration until the levels are in perfect adjustment. 

To Adjust the Needle to the '''■Dipy While the comxDass 
is still in a perfectly level condition, see if the needle is in a 
horizontal plane. Should this not be the case, move the small coil 
of wire towards the high end until the needle swings horizontally. 

To Adjust the Sight- Vanes. Observe through the slits a 
fine hair or thread made exactly vertical by a plummet. Should 
the hair appear on the side of the slit, the sight-vane must be 
adjusted by filing its under surface on the side that seems the 
higher. 

To Adjust the Needle. Having the eye nearly in the same 
plane with the graduated rim of the compass-box, bring one 
end of the needle in line with any i3i-ominent graduation mark in 
the circle, as, for instance, the zero or the 90-degree mark, and 
notice if the other end corresponds with the same degree upon the 
opposite side; if it does,.- the needle is said to "cut" opposite 
degrees; if not, bend the center pin, until the ends of the needle 
are brought into line with the opposite degrees. 

Then, holding the needle in the same position, turn the 
instrument half-way round, and note whether the needle now cuts 
opposite degrees ; if not, correct one-half the error by bending the 



74 PLANE SURVEYINa 

needle, and the other half by bending the center pin. The 
oxjeration of testing and correcting should be repeated until perfect 
reversion is secured in the first position. - This being obtained, the 
operation should be tried on another quarter of the circle ; if any 
error is found, the correction must be made in the center pin only, 
the needle being already straightened by the jprevious operation. 
When the needle is again made to cut, the test should be tried in 
the other quarters of the circle, and the correction made in the same 
manner, until the error is entirely removed and the needle will 
rt'V(!rse at every point of the graduated circle. 

Use. In the oi^eration of locating points, and therefore lines, 
by angle-measuring instruments, two operations are necessary: — 
(1 ) to measure the angle at the instrimient between some given line 
and the line jDassing through the given point; (2) to measure the 
distance from the instrument to the given point. For the first 
operation two tyjjes of instrument are in general use — the 
compass and the transit. For the compass, the line of reference 
from which all angles are measured is a meridian, and the angular 
deviation from this line is called the bearing. The bearing and 
length of a line are collectively named the course. The comiDass, 
therefore, measures bearings directly and angles indirectly. 

To Determine the Bearing of One Point from Anothei\ 
"Set up" th(! compass over one of the points, and level carefully. 
Turn the sight-vanes in the direction of the second point, tvith the 
north end of the plate ahead. Hold a rod upon the second point, 
and cover it with the slits in the sight-vanes. Now lower the 
needle u^xjn the pivot, being sure that the instrument is still level; 
allow it to come to rest, and read the bearing. 

To Survey a Series of Lines 'with the Compass. "Set up" 
the comiMss over the point A, with the north end of the plate 
ahead (Fig. 58); and after leveling, tiirn the sight-vanes to cover 
a rod held upon the x^oint B. Now send out the tape in the direction 
of B, and, sighting throiigh the slits, signal the head tapeman 
into line. Continue this until the point B is reached. Now read 
and record the bearing and the length of the line. Take up the 
instrument, and carry it to B. Set it ujd over B, with the north end 
ahead, that is, i^ointing in the direction of the survey. Level, and 
turn \\w south end so as to cover a rod held iipon the point A. 



PLANE SUKVEYIXG 



Read the bearing as a check upon the former one, Init reversed iu 
direction; /. r'., if the bearing from A to B was north by east, the 
bearing from B to A will be south by west. It' the direct and 
reversed bearings clieck, turn the north end of the compass to cover 
a rod held uxjon C. Read the bearing, measure B C, take the 
instrament to C, and j)roceed as before. 

If at any station, such as C, the direct and reversed bearings 
do not agree, take the instrument back to B and again take the 
bearing of B C If they still disagrei> it indicates local attraction 
at C. Take the instrument to D and take the bearing of D C, 




comparing it with the bearing of V D. If these disagree, record 
the bearings of B C and D C as well as those of C B and C D. 
The latter should check th(i former, since the local attraction at C 
will affect both lines equally; and the correct angle between the 
lines can be computed. 

Locating a series of lines with certain lengths and bearings is 
essentially the same as above, except that after the compass has 
been turned in the proper direction, the stations must be brought 
into proper line. 

Here it may be well to remark upon the proper method of 
reading and recording bearings. Always read the north or south 
end of the plate first; /. e., if a line has a bearing 35° east of 
north, it should be read and recorded N 35° E. If the bearing is 
90° east or west of north or south, record the bearing as E or W. 

The Gunter's chain is always used iu lan<l surveys made with 
the compass, and deeds and records of such surveys are based 
upon the Gunter's chain as the unit. 

11/ lit s lierjardhig the Use of the Compass. Sometimes, as 
when the line of which the bearing is required consists of a fence, 



PLANE SURVEYING 



t'tc, the fouipass cannot be set upon the line. In such a case 
measure oti' ecpial distances at riglit angles to thi' line, and tind the 
l)earing of the parallel line; the length should be nif asured upon 
the line itself. In other cases it may be more convenient to set 
the compass or rod "in line" upon the line produced, or upon some 
intermediate jjoint of the line. 

It is more important to have the compass level, crosswise of 
tlie sights, tiian parallel with them. 

Avoid reading the bearing from the wrong number of the two 
between which the needle points, as for instance 35^ for 2."j . 

Check the vibrations of the needle by gently raising it off the 
pivot and lowering it again by means of the screw on the under 
side of the box. 

If the needle is slow in starting, smartly tap the compass to 
destroy the effect of any possible adhesion to the pivot or friction 
of dust upon it. 

Avoid holding the pins, axe, or any other body of iron, in 
close proximity to the needle. 

Should the needle adhere to tiie glass after the latter has been 
dusted with a handkerchief or has been carried so as to rub 
against the clothes, the trouble is due to the glass being thereby 
charged with electricity and may be obviated by moistening the 
finger and apjilying it to the glass. 

RELOCATION. 

Suppose it is required to relocate a line, no trace of the old 
survey being at hand exceiDt the given line. Now, between the 
dat(! of the old survey and the present, the declination of the needle 
has changed several degrees. The first duty of the surveyor is to 
consider this question very carefully, and to ascertain the i)robable 
amount of change in the magnetic needl(!. SupjMse the result of 
his inquiry leads to N 38° 15' E as the bearing. Starting at 
corner A, Fig. 59, the surA-eyor runs a random line AS on the 
bearing N 38° 15' E, and measures along this line a distance of 
32 chains, or 2,112 feet, to point S. On arriving at S, the surveyor 
proceeils to look over the ground on both sides of this point for a 
lost comer, which is describi'd in the old record as a monument, 
stum]), or some other well-defined mark. If, after diligent search, 



PLANE SURVEYING 



no trace of this mark can be found, nothing fnrther can be done 
from the data at hand. However, should the mark be found at nt, 
a perpendicular is dro^Dped upon the line AS, and its length is 
'^ , s measured, as is also the distance «S. 

; Jk It is now evident that the distance 

I ^^ ,3^ Kn becomes known. From the right 

1 ^-^^''' triangle, the angle nKm can be com- 

1^;-^^' puted, and the jjresent magnetic bear- 

Fig. .'")9. ing of Am can be determined. 

For example, suppose tliat mil is found to be 37.4 feet, while 

A« is 2,110.5 feet, then tan. /*A;h. =— ,^ =- 0.01772, whence nKm. 

=1° 10', and the present magnetic bearing of Km is N 37° Ki'. 

The distance A;h == "^^Aj^ = 2.110.8 feet. This indicates 

cos. 1 10 

that the present work is correct, and that the old survey was in error 

by 1.2 feet. As there is a princi]jle of law that establishes corners 

and moniiments, resurveys miist control ; therefore the new record 

of the line A/« is N 37° 1(>' E, 2,110.8 feet. Intermediate points 

of the line A/w, may now be established from the starting point A, 

running it out with the new bearing. 

EXAMPLE FOR PRACTICE. 

Compute the distance and bearing of two points which are not 
intervisible. Call the line GH. A line is run approximately iu»ar 
H, from the known corner G to a x^oint A which is visible to H; 
the bearing and length of this line being N 42° 15' E, 714.5 feet; 
AH being N 1° 08' E, 210.5 feet. 

Ans. N 33° 14' E, 883.99 feet. 

To Find the Bearing of One Line to Another. Suppose, in 
Fig. fiO, that of the tract of land therein described there has been 
prepared a rough plot upon which the angles, bearings, and 
distances as taken from the field book are figured. In order to find 
the bearing of one line to another, add together the interior angles 
formed at all the corners; call their sums a; multiply the number 
of the sides by 180°; from the product subtract 360°. If the 
remainder is equal to «, this is proof that the angles have been 
accurately measured. This, however, will rarely if ever occur; 



78 



PLANE SURVEYING 



tliLTe will jilwiiys bu some discrepancy, but if the tiekl work has 
boeu perfoniu'il with reasonable euro the discreptuicy will not 
exceed two minutes for each angle. In this case divide it, in equal 
parts, among all the angles, adding or subtracting, as the case may 
be, vmtil it amounts to less than one minute for each angle, when 
it may be entirely disregard(>d in couunon farm surveys. 

The corrected angles may now be marked on the j^lot in ink, 
and the penciled figures erased. We shall suppose the corrected 




Fig. «). 



ones to be as shown in Fig. (JO. Next, by means of these corrected 
angles, correct the bearings also. 

Select some side, the longer the better, from two ends of which 
the bearing and the reverse bearing agree, thus showing that the 
bearing was probably not influenced by local attraction. Let side 
2 be the one so selected; assume its bearing N 75° 32' E, as taken 
on the ground, to be correct; through either end of it, say at its 
farther end 2, draw a short meridian line, parallel to which draw 
others through evt>ry corner. 

Now, having the bearing of side 2, N 75° 32' E, and requiring 
that of side 3, it is plain that the reverse bearing from corner 2 is 
S 75° 32' W, and that therefore the angle 1 2 m is 75° 32'. 
Therefore, if we take 75° 32' from the entire corrected angle 1 2 3, 
or 144° 57', the remainder 69° 25' will be the angle m 2 3; conse- 
([ucntly the bearing of side 3 must be S 69° 25' E. For finding 
the bearing of side 4, we now have the angle 2 3 a of the reverse 



PLANE SURVEYING 



Ix'iiring of side 3, also eiiual to 69° 25', and if we add this to the 
entire corrected angle 2 3 -4, or to 69° 32' we have the jxngle a 3 4 
=: 69° 25' + 69° 32' = 138° 57', which, taken from 180°, leaves 
the angle 5 3 4 = 41° 3' : consequently the bearing of side 4 must 
beS41°3'W. 

For the bearing of side 5, we now luive the angle 3 4 c = 41° 
3', which, taken from the corrected 
C angle 3 4 5, or 120° 43', leaves the 
angle c 4 5 = 79° 40', consequently 
the bearing of side 5 mnst be N 79° 
40' W. At corner 5, for the bearing 
of side 6, we have the angle 4 .5 d = 
JD T9° 40', which, taken from 133° 10', 
leaves the angle c/ 5 6 ^ 53° 30'; 
conseqiiently the bearing of side 6 
must be S 53° 30' W; and so with 
each of the sides. Nothing biit carefnl observation is necessary to 
see how the several angles are to be employed at each comer. 




Pis. 61. 



FARM SURVEYING. 

Method of Progression. Farm surveying with the compass 
does not differ in any essential particular from the methods 
outlined for surveying a series of lines. If the boundary lines are 
irregular, it will be necessary to measure offsets at projjer intervals, 
that the included area may be calculated. The method above 
described is known as the method of jwogTession. 

Method of Radiation. The method of radiation consists in 
setting up the instrument at some point inside or outside the field, 
from which all the corners are visible and accessible, and then 
measm-ing the bearing and lengths of the lines to these corners. 
Fig. 61 illustrates the method. Set up the compass at the point O, 
and take the bearings and lengths of the lines O A. O B, O C. 
O D, and O E. 

Method of Intersections. Lay off a base-line of convenient 
length inside or outside the field, from which all the corners are 
visible. Set up the compass at one end of the base-line, and take 
the bearings from it to each corner in succession. Remove the 



80 PLANE SURVEYING 

compass to the other end of the base-line, and take the bearings 
from it to each comer in succession. Take the bearing and leagtli 
of the base-line. Now, when these bearings and lengths are 
plotted, the intersections of tlie lines will define the corners. 

Proofs of Accuracy. When the survey of a field is plotted, 
if the end of the last course meets the starting x^oint, it proves tlit^ 
"work, and tlu' survey is then said to "close." Errors of closure 
nui}' bi- due either to incorrect lengths of lines or to incorrect 
bearings, or to both. 

Diagonal lines running from corner to corner of a field may 
be measured and their bearings taken. When these are plotted, 
their meeting the points to which thej- were measured proves the 
accuracy of the work. 

Finally, the accuracy of the work may be tested by calculating 
the "latitudes and departures" of all the courses. If their algebraic 
sum is etpial to zero, the work is correct. A check u^jon the 
bearings may be had by calculating the "deflection angles" between 
the courses. If their sum is equal to 3()0 degrees, the bearings 
are correct. This, however, will seldom be the case. A certain 
amount of error is ])ermissible, depending upon the; nature and 
importance of tin; work. 

Field Notes. The field notes may be recorded in various ways, 
the object being to make them clear and full. 

1. Tlio surveyor may make, in the field book, a rough sketch 
of the survey by eye, and note on the lines their beariugs and 
lengths. If a protractor and scale are available, the actual bearings 
and lengths of tin; lines may be plotted in the notebooks, as well 
as offsets, etc. 

2. Draw a straight line uji the page of tlie notebook, and 
record on it tlu; bearings and lengths of the lines. Offsets, 
tie-lines, etc., can be plotted in tlieir proper positions. 

3. Write the stations, bearings, and distances in three 
columns. This method has the advantage, when applied to farm 
surveying, of being convenient for use in the subsequent calcula- 
tion of contents, but does not give facilities for noting effects. It 
is illustrated as follows: 



PLANE SURVEYING 



81 



ST.\T10NS. 


13E.\BI>-GS. 


DISTANCES. 



1 
3 
i 


N. 32° E. 
S. 36^ E. 
S. 271^° W. 
S. 16' W. 


1G.82 

18.90 

7.85 

15.30 



Notice tluit distances are giveu iu Guuter's chains, and in 
calculating content the result will be given in square chains, which 
can be reduced to acres by pointing off one decimal place. 

To Change Bearings. In ci'rtain kinds of work with the 
compass, it is convenient to assiime one of the lines as a meridian, 
and it then becoines necessary to change the bearings of all of th(^ 
other lines to conform witli the assumed meridian. This case is 
best illustrated by an example. 

The bearings of the sides of a tick! are here shown: Suppose 
now tliat the first course is assumed as a meridian, that is, that its 



STATIONS. 


BEARINGS. 


DISTANCES. 


1 

2 
3 
4 
5 


N. 35° E. 
N. 831^° E. . 
S. 57° E. 
S. 3414 - W. 

N. 561^° W. 


2.70 

1.29 
2.22 
3.55 
3.23 



bearing is due north and south. RequinHl the bearings of the 
remaining courses. 

Since the courses are changed to the west by 35°, the new 
bearing of course 2 will be N 48^° E. Of coiirse 3 it will be 
57° + 85° = 92°, or the new bearing will be N 88° E. Of course 
4 it will be 34^° — 35°, or f ° in the next quadrant, or the bearing 
will be S 1° E. Of course 5 it will be 56^° + 35° = 91^°, or the 
bearing will be S 88|° W. 



EXAMPLE FOR PRACTICE. 

The bearings of a series of courses are given as follows: 
The bearing of the first course is changed to due north and south. 



82 



PLANE SUKVEYING 



] t is required to determine the bearings of all the courses, due 
to this change. Find bearings and plot the lines. 

Ans. Course2 — N62|° E; 3 = N9° W; 4 = N68° W. 



STATIONS. 


UKAKINC.^. 


DISTANCES. 


■1 

2 
.3 
4 


S. 21° W. 
N. 8,3 V4' K. 
N. 12° E. 
X. 47= W. 


12.41 

5.80 
8.2.-) 
4.24 



Latitudes and Departures. The latitude of a point is its 
distance north or south of some line takenasa^jf.-rrt^^e/ of latitude^ 
or line running east and west. 

The longitude of a \iomi is its distance east or west of some 
line taken as a men'dian, or line running north and south. 

The distance that one end of a line is north or south of the 
other end is the '' Difference of Latitude" of the two ends of the 
line, and is called its northing or southing, or its latitude. 

The distance that one end of a line is east or west of the 
other end is the " Difference of Longitude " of the two ends of the 
line, and is called its easting or westing, or its departure. 

The terms Latitude Difference and Longitude Difference have 
of late come into (piile general favor; but while tlicy are perhaps 
more es])licit, t\u'j are certainly cumbersome, and the older terms 
will bo adhered to in what follows. 

N A In Fig. (■)2, N 8 represents a meridian. 

and E W a parallel of latitude. If we 
take the lino O A, its bearing as given 
by the comi^ass is the angle NOA. The 
latitude or northing of thc^ point A is 
tlienforo A B = O A cos NOA. Its 
departure or easting is O B = A sin NOA. 
To find the hitiii/ifr of a course, 
multiply the length of the coTirse by tlie 
natural rrt.sv'/u' of tlu' bearing; and to find 
Pitf. 02. the^Ay*;^/'/*//'!- of any course, multiply the 

li'iiglli of the course by tlie iialural .v///r of tile bearing. 



w-J^ 




PLANE SURVEYING 



83 



If the course be northerly, the latitude will be north, and will be 
designated by the sign -{-, or xjIus; if the course be southerly, the 
latitude will be south, and will be di>signated by the sign — , or minus. 

If the course be easterly, the depai^ure will be east, and will be 
designated bj' the sign +, or phis; if the course be westerly, the 
departure will be west, and will be designated by the sign — , minus. 

Thus in the figure, OA is of plus latitiid(> and plus departure; 
OP is of plus latitude and minus departure; OD is of niiniis 
latitude and minus departure; and OC is of minus latitude and 
plus departun-. 

For calculating latitudes and departures, a set of traxerse 
tables may be procured; but a table of natural functions will be 
satisfactory, though possibly less convenient. 

Testing a Survey by Latitudes and Departures. It is evident 
that after the siirveyor has gone completely romid a field or farm, 
measuring all the lengths and bearings, returning to the starting 
.point, he has gone as far north as soiith, and as far east as west. 
In other words, if the work has been done correctly, the algebraic 
sum of the latitudes must equal zero, and the algebraic sum of the 
departures must equal zero. This condition, however, will seldom 
be attained, and it becomes necessary to decide how much error 
may be permitted without necessitating another survey. This will 
depend upon the nature of the work and its imi^ortance, and a 
siirveyor will soon determine for himself his factor of error, 
depending partly upon his instrument, partly upon personal skill. 
for ordinary cases. If it is necessarj' to depend upon a "green" hand 
to carry the tape or chain, this may prove a fruitful source of error. 

We shall now proceed to calculate the latitudes and departures 
of the sun'cy as given below. Arrange the diagram as below with 
seven cohinins: 



STATIONS. 


i;v.\rA::< -. 


il- I'ANt'KS. 


LATITUDES. 


DEPARTURES. 


N. 


s. 


E. 1 W. 


1 

2 
.-i 

i 


S. 21 ~ AV. 
xV. 8:5^4° E. 
X. 12' E. 
X. 47 W. 


12.41 
5.86 
8.25 
4.24 


0.091 
8.069 
2.892 


11.591 


5.819 
1.710 


■l.Jl.T 
3. KM 






30.76 


11.652 


11.591 


7.535 


7.547 



84 PLANE SURVEYING 

The cosine of the bearing of course 1 is 0.934.12.41=11.591 — Latitude. 
The sine of the bearing of course 1 is 0.358.12.41= 4.443 — Departure. 
The cosine of the bearing of course 2 is 0.118.5.86 = 0.691 -[-Latitude. 
The sine of the bearing of course 2 is 0.993.5.86 = 5.819 + Departure. 
The cosine of the bearing of course 3 is 0.978.8.25 = 8.069 -r Latitude. 
The sine of the bearing of course 3 is 0.208.8.25 = 1.716 + Departure. 
The cosine of the bearing of course 4 is 0.682.4.24 = 2.892 + Latitude. 
The sine of the bearing of course 4 is 0.732.4.24 = 3.104 — Departure. 

The latitudes fail to balance bj' O.ORl chains, and the departures 
by 0.012 chains. The error of "closure" of the sur\-ey is therefore 



E=-y|.061 + .012 = 0.062 + chains, or approximately 4.09 feet. 
This sum may be divided up among the courses in proportion to 
the length, or the bearings may be corrected, or partly one and 
partly the other, as will hereafter be explained. 

Balancing the Survey. Before proceeding to the calculation 
of the content of a field or farm, the survey must be balanced; 
that is, the latitudes and departures must be corrected so that their 
sums shall be equal, or shall balance. As to whether the bearings 
or lengths shall be corrected, will depend somewhat uj)on the 
conditions undi'r which the survey was made. If the surveyor has 
reason to think that the error is entirely in the bearing of one or 
more, or even of all of the courses, the corrections may be made 
accordingly. If, On the; other, hand, one or more of the courses 
were measured over difficult ground, it may be presumed that the 
error occurretl in those lines. If, however, there is no reason to 
believe that one course is in error more than another, the 
differences may be distributed among the courses in proportion to 
their length, according to the following pro^xirtions: 

As the length of any course is to the sum of the lengths of all 
the courses, so is the correction of the latitude of that course to 
the total error in latitude of all the courses. 

xis the length of any course is to the sum of the lengths of 
all the courses, so is the correction of the departure of that course 
to the total error in dej)ariure of all the courses. 

The practical application of these pro^xirtions to balancing a 
survey will be illustrated from the preceding ijroblem: 

For course 1 . . . . 12.41 : .30.76 :: .r : 0.061 ....x = .0246, correction for latitude. 
For course 2. . . . 5.86 : 30.76 :: x : O.OCl r = .0116, correction for latitude. 



PLAXE SUKVEYINQ 85 

For course 3. . . . 8.25 : 30.76 :: x : 0.061 c = .0164, correction for latitude. 

For course 4. . . . 4.24 : 30.76 :: .r : 0.061 r = .0084, correction tor latitude. 

Since the sum of the north latitudes is the greater, the corrections will be 
subracted from them and added to the south latitudes. That is to say, the 
correction for course 1 will be added to 11..591, the result being 11.6156. 
The correction for course 2 will be subtracted from 0.G91: that for course 3 
will be subtracted from 8.069; and so on. 

For cour.se 1. . .12.41 : .30.76 :: .r ; 0.012. . .x = .0048, correction for departure. 
For course 2. . . 5.86 : .30.76 :: .r ; 0.012. . .x = .0023, correction for departure. 

For course 3. . .. 8.25 : 30.76 :: x : 0.012 r. = .00.32, correction for departure. 

For course 4.. .. 4.24 : .30.76 .. x : 0.012 c = .0017, correction for departure. 

The corrections are to be subtracted in this case from the west departure 
and added to the east departure. 

In thi.s example, the errors are small, bat often they will be so 
large as to raise doubt as to the accnraey of the survey. In such a 
case, go carefully over all the computations, and, if the error is still 
too large, check the exterior angles of the figure (their sums 
should equal 360°), and if necessary repeat the survey. Having 
corrected the latitudes and departures, the corrected bearings of the 
courses may be dedticed from the trigonometric ratio: 

rp v, . • corrected departure 

' ' ' "^ corrected latitude 

Calculating the Content. After a field has been surveyed, its 
content may be calculated by dividing it up into triangles, trape- 
zoids, etc., calculating the various contents, and adding them 
together. This, however, is at best a cumbersome method, involv- 
ing much work of calculation and great chance of error. The 
method of latitudes and departures is at once sim^Dle, easily applied, 
and easily checked. 

Before proceeding to develop a formula for this method, it will 
be necessary to illustrate and define certain terms. 

Draw a line, as N S (Fig. 63), through the extreme east or west 
corner of the field for a meridian. From the definitions previously 
given, the difference of longitude of the two ends of a line is the 
departure of the line. I B is therefore the departure of the line 
A B. The departure of the line B C is L C; that of E F is S P; 
and that of A F is O Q. 

The perpendicular distance of each station from the given 
meridian is the longitude of that station, plus if east, minus if 



86 



PLANE SlTfYEYING 




west. Thus the longitude of A is zero; that of B is I B: that of C is 
I B + L C; that of E is O Q + F 8; and that of F is O Q = 
ZS — FS. 

The difference of latitude of the two ends of a line is called the 

latitude of the line. Thus the 
latitude of A B is A I: that 
of BC is BL; that of E F 
isES. 

The distance of the middle 
of any side of a field from the 
meridian is called the longi- 
tude of that side. Thus the 
longitude of the side A B is 
GH; thatof BCis JX=:GH 
+ KM + MX; and that 
of A F is WV = OK — QK 
Fig. (>i. — QP^ the minus signs being 

used ill this instance because the lines E F and A F bear to 
the west. An analysis of W V will show that it equals O K 
(longitude of preceding course) + [ — R Q (one-half departure of 
preceding course)] + [ — QP (one-half departure of the course 
itself)]. 

To avoid fractional quantities, double the preceding esiires- 
sions and tlien deduce a general rule for finding double longitudes. 
The double longitude of the first course equals the departure 
of that course. The double longitude of the second course equals 
the double longitude of the first course, plus the departure of the 
first course, plus the dej)arture of the second course. 

The double loiujitude of any course equals the douhle longi- 
tude <f the preceding course., ])lu8 the departure of the preceding 
course, plus the departure of the course itself. 

We shall now proceed to deduce a rule for determining areas 
by double longitudes and dejiartures, and shall first take a three- 
sided field, as in Fig. 64. 

Drawing a line through the most westerly corner A, we see 
that the area of the field will be the difference between the area of 
the traix-zoi<l D B C M and the combined area of the triangles 
DBA and A C ^M. The double area of the triangle D B A is the 



PLANE SURVEYIXG 



87 



protluot of D B bj- D A, or tlu- doubk- longitude of A B by the 
latitiuli' of A B. The resulting proiluct will be north or ^/;'.v. 
The doiible area of the trapezoid D B C M is the ijroduct of (D B 
+ 31 C) = 2 G H, by D M, that is. the doiible longitude of B C by 
its latitude. The resulting product will be south or ;«//!(«. The 
double area of the triangle A C ]M will ho tlie product of !M C by 





Fin. <ji. 



Fiff. 6.5. 



A M, or the double longitude of the course A C by its latitude. 
The residting product will be north or plus. Adding together, 
then, the phis products, and subtracting from the miniis i^roduct, 
gives as the resiilt the double area of the field. 

We shall next take a four-sided field, as in Fig. (m. 

It is evident that the area of the field A B C D is the difference 
between the sum of the areas of the two trapezoids T B C R 
and R C D E and the sum of the areas of the triangles A B T 
and A D E. 

The double area of the triangle A B T is the jjroduct of B T 
by A T, or the double longitude of the course A B by its latitudi'. 
The resiilt will be a north prodiict or j)ltf 6-. The double area of the 
trapezoid T B C R will be the product of (T B + C R) = 2 L P 
by T R — that is, the double longitude of the course B C by its 
latitude. The result will be a south product or mi nun. The double 
area of the trapezoid R C D E will be the product of (R C + D E) 
= 2 F K, by R E, or, the double longitude of the course C D 
by its latitude. The result will be a south product or minus. The 



SH. 



PLANE SURVEYING 



STA- 


BEARINOS. 


Distaoces. 


LATITUDES. 1 DEPARTURES. 


DOUBLE 
LONGI- 
TUDES. 


DOUBLE AREAS. 


TIONS. 


N. 


s. 1 E. 


w. 


i N- 


s. 


1 


S. 21' W. 


12.41 





11.616 


4.438 


4.4,38 




.51.552 


2 


N.83i4'E. 


5.86 


0.679 


5.821 




5.821 


3.952 




.T 


N. 12' E. 


8.25 


8.05.3 


1.719 




13.361 


: 107. 596 




i 


N. 47' W. 


4 24 


2 884 




3 102 


11.978 


34.545 

















146.093 51.. 5.52 
51.552 



94.541 
47.271 



Akea =^ 47.271 S(|. Chs. = 4 aorps 2 roorls 37 sq. ppi-fhr-s. 



donbli> circa of the triangle A D E will be the product of E D by 
A E, or the double longitude of the conrse A D by its latitude. 
The result will Ix- a north product or jiIh.s. Finally, adding 
together the nortli x.)roducts, adding together the south products, 
and taking tlie difference of their siuns, gives as the resiilt the 
double area of the field A B C D. 

The same ^jrinciple will apply to any enclosed area, however 
great the number of the sides. T/ie area leill always he oiw-half 
the difference of the sums of' the north and the south products 
arisiiKj from rniiltiphihuj the doidde lonf/ltude of eacli course hy 
its 1/it'itiitle. 

For systematic computation arrange the work as follows: 

.\rranf;e the columns as in the jirobletn on page 8.3. 

Balance the latitudes and departure.s, putting the eunected i|uantitios 
above the others in red ink: or else arrange four additional columns, and enter 
them in their proper places. 

Compute the double longitude of each cour.se with reference to a 
meridian passing through the extreme east or west station, and jilace the 
results in another column. 

Multi])ly the double longitude of each cour.se Ijy the corrected latitud<' 
of that course, and place north iiroduet-- in one column and south products in 
another. 

Add together the north jiroaucts and also the south products, ana take 
the difference of their sums. Divide the difference by two, and the result 
will be the area desired. 

If the survey has been made with a (uinter's chain, the result will be 
in .-iiiuare chains. Divid<' by ten t(j reduce to acres. 



PLANE yUKVEYlNil 89 

To test the correctness of the calculation assume the meridian as passing 
through the extreme station upon the other siile of the tieUl, and carry out 
the work in detail as before. 

We shall now proceed to calculate the content of the field 
given by the notes on page 83. The corrections to the latitudes 
will be foimd on page 84, and the corrected deijartures on page 85. 

The arrangement of the columns for convenient calculation is 
as described on page 88. Upon making a rough sketch of the 
course, it is found that station 2 is the farthest east; and therefore 
the double longitudes will be calculated beginning with course 2. 
From the definition previously given, the double longitude of 
course 2 is equal to its departure, = + 5.821. The double longi- 
tude of course 3 equals the double longitude of course 2, plus the 
departure of course 2, plus the departure of course 3, = 5.821 -(- 
5.821 + 1.719 = + 13.361. The double longitude of course 4 
equals the double longitude of course 3, plus the departure of 
course 3, plus the de]jarture of course 4, =: 13.361 + 1.719 + 
{— 3.102) = + 11.978. The double longitude of course 1 
equals the double longitude of course 4, jjIus tlie dej^artm-e 
of course 4, jilus the departure of course 1, = 11.978 + 
(— 3.102) + (— 4.438) = + 4.438. Multiplying these double 
longitudes by their resjoective latitudes gives the quantities in 
the last two columns, the first being a south product or negative, 
and the other three being north products or positive. Taking the 
difference of the sums of the quantities in these columns and 
dividing the result by two, gives the content of the field, 47.271 
square chains. Dividing by ten gives 4.7271 acres. Reduce to 
roods and i^erches, by multiplying the decimal x^art by 4 and 40 
successivelj'. 

The result maj' now be checked by beginning witli tlie most 
westerly station, and it will be necessary to recalculate the quantities 
in the last three columns. 

The following problems are taken from '"Glillespie's Surveying" 
(Staleyj: 

EXAMPLES FOR PRACTICE. 

Calculate the content of the fields from the data tabulated 
below. The result, where found in square meters, should be 
reduced to acres: 1 sq. metre = .000247 acres. 



90 



PLANE SURVEYING 



(1) 



.STAIID.NS. 



BEARINGS. 



DIST \XCES. 



1 


X. 3iV4° E. 


2.73 


2 


X. 85"' E. 


1.28 


3 


S. 56»4= E. 


2.20 


4 


S. 34^'- W. 


3.53 


o 


X. 561^" W. 


3.2() 



Alls. 1 acre, roods. 14 perches. 



HEARINGS. 



niSTANCES. 



X. 35° E. 
X. 831^' E. 
S. 57° E. 
S. 34 14- W. 
X. 56J^° W. 



2.70 
1.29 
2.22 
3.55 
3.23 



Alls. 1 acre, roods, 15 perches. 



HEARINGS. 



9 
10 
11 
12 



S. 5 
S. .39 
S. 50 
S. 79 
S. 53 
S. 48 
X.82 
S. 87 

X.84 
S. 5 
N.84 



35- W. 
35' \V. 
25' E. 
5 E. 
50' E. 
15' W. 
45' E. 
' 40' E. 

= 25' W. 
:3o' W. 
25' W. 



DISTANCES. 



2,:«8 

1,060 

.3,078 

325 

275 

200 

450 

186 

8,768 

1,898 

.3,.530 

257 



.88 meters 
.27 meters 
.31 meters 
.00 meters 
00 meters 
00 meters 
.00 meters 
72 meters 
.12 meters 
54 meters 
.60 meters 
.50 meters 



acres. 

roods. 

-^ sq. rods. 

Supplying Omissions. The method of latitudes and depar- 
tures may be applied to supplying any two omissions in the field 




PLANE SUKVEYINU 



notes, as will lie e^xplaiiUMl in roiiiicotioii with the "Use oi the 
Transit." 

Azimuth. Tlie azimuth nf a line is the liorizoutal ant^'le 
whieh tlie line makes with some other line taken as a meridian. 
It ditt'ers from bearing in that it is measured continuously from 0" 
to 360°. All descriptions of property nmst be given in terms of 
bearings, but line surveys with either the eomjiass or the transit 
had better be given in terms of the azimuth. 

In astronomical and geodetic work it is customary to reckon 
azimntli from tlie j</iii//i jxiiiif (irnimd IhntiKjh I he irrxf, through 




Fi.'. GO. 



300°. For the ordinary operations of surveying, jujwever. it is 
better to measure the aziniutli from tlic nortli ]i()iat to the ri.nlit 
througli 3r,0°. 

RESURVEYS. 

"Where the boundary lines of a farm or town have been obliter- 
ated and the comers lost, it is often necessary to make 
resurveys in order to re-establish them. If the corners can be 
found by reliable evidence, they must be accepted as corners e\cn 
though the second bearings and lengths of tlie lines indicate 
different points. 

It sometimes happens that some corners can be fomid wliile 
others cannot. In such cases a series of random lines is to be luu 
with the old bearings, or with the old bearings corrected for a 
change in declination of the needle between the two dates. 

As an example, let the records in an old deed give tlie lengtli 
and bearings of three lines as follows; (See Fig. C)C}.) 



92 PLANE SURVEYING 

A& N 60" E 10 chains. 
be N 45° E 4 chain.s. 
cd S 45" E 8 chains. 

There being no definite data at liaiid to determine the change 
in tlie magnetic declination between tlie dates of the two sxirveys, 
the lines AB, BC and CD are run with the given bearings and 
distances from the known corner A. The old corners i and r 
cannot be found; but on arriving at D the old corner f7 is discov- 
ered at a point 20.4 links S and 12" W from D It is I'ccinircd to 
locate tile old corners h and c. 

By tile metliod explained before, tiie lengtiis of tiie lines DA 
and (/A may ho computed. They are: for DA, south 82° 47', west 
17.29 chains; for if A, south 83° 26', west 17.22 chains. 

Now tlie t-rror T>(J between the two corners is due to two 
causes: (I) the continued variation in the magnetic bearings of the 
old surv'eys, (2) the diffei'ence in the length of the chains used. 
The first cause alters the polygon Ahct/A around the point A by a 
small angle. The second cause alters the length of the sides in a 
constant ratio. The differtmce between the bearings DA and (/A 
is the constant angle, wliile the ratio of the length of tiie old lines 
is the constant ratio. To find tiie bearings of the old line, there- 
fore, eacli of the given bearings is to be corrected liy tiie amount 
8T 2C>' minus 82° 47' == 0° 39'. To find the lengtli of the old 

17.22 

lineea<'li of tliegiven lengtiis is to be nniltiplied l)y - " = 0.99(). 

(Supixjse now tliat tlie work of computation lias been done 
witli such precision that tlie error in cliaining must be regarded as 
lying in the old survey. A^jplying these results, we find the 
adjusted bearings and lengths of the old line to be, 

A/> = N 00° 39' E 9.9r. chains. 

/>r = N 45° 29' E 3.99 chains. 

r,f =S 44° 21' E 7.97 chains. 
With the new data tlie line may be rerun and tlu> corners h and r 
located, a check on the field work being that the lost line should 
end exactly at d. 

It is, however, not difficult to coniputi^ the lengtli and bearings 
of B h and C r. so tiiat h and v may be located from the points 
B and C. 



PLANE SURVETma mi 

The ijriiiciple for doing tliis is tliiit the polygons A B C D A 
inicl A 1) c d X are similar: thus tlu' triangles A B // and A D d are 
similar; hence the length B h is 

Bl>=-Dd ^ ^ = j^^ = ll.cS links. 

Al^ *lu' angle AB ^> = the angle A' D d or 70^ 47': hence the 
Learingof B /; is S 10° 47' E. 

In like manner, the triangle A B ?< being similar to A D d, the 
length and bearing of A D are first computed. The distanci' C c is 
1(1.4 links, and its bearing is S 15° 03' E. The lines B h and C c 
are now nui from B and C, and thus the most probable location of 
the old corners b and <■ is determined 

EXAMPLE FOR PRACTICE. 

The records of an old stirvey read as follows: 

"Commeucing at a point marked No. 5 and running N fi2° E 
14 chains to a stake marked A, thence running N 43^° E 800 
chains to a stake marked B, thence N. 5° W. 12.00 chains to a 
stake C, thence N 721° E. 10.25 chains to a stake D, thence S 
12° W (5.43 chains to a stake marked No. 3. On rinming the 
lines, the end of the last one, instead of being at a stone marked 
No. 3, was 0.62 chains due E from it." Find the adjusted bearings 
and lengths of the old lines; also find the distance and din ctioii 
from each station of the new survey, and the corresponding corner 
of tl - old. 

Ans. N 78° 0(i ' W 2(i links for A ; S 74° 35 ' W 5G links for C. 

DIVISION OF LAND. 

The first problem to be considered is that of dividing a field 
into two given parts by a line starting from a given point. For 
exami)le, let it be required to draw from the point D, Fig. ()7, a 
line D P in such a position that the area of B c D P shall be 5 
acres or 217,800 square feet. 

The solution of the problem involves the finding of the dis- 
tance from A to P or B to P, and of the length of the azimuth of 
the dividing line D P. Let a line be drawn from D to the corner 
A, and suppose that the ai'ea A B c D A can be foimd. Then the 



94 



PLANE SITEVEYINCI 



area of the triangle A P D is known, as this is equal to A B r- T> A 
niintis 5 acres. The longitude d D of the point D is also known; 
hence the length of A P is 

A P = 2 acres of A P D A divided by ,/ D; then P B = A B 
— A P. Tlu' length and azinuith of D P are finally comxouted 
from the right angled triangle tl D P. To jjerform the comimtation 

for finding the area of A B r DA, 
the adjusted latitiide and longitude 
deijartnres of the courses from 
\e: A to D are to be taken. The 
latitude and longitude departures of 
the course D A is then found from 
the ijriuciple that the sum of the 
northings equals the sum of the 
southings; and the longitude depart- 
iire of D A is supplied in like 
manner. Comxjleting then the com- 
putation, the area of A B e D A is 
found to be 2S(i.(;88.7 scpiare feet_ 
The area of the triangle A D P is this quantity minus 217,8(X) 
siiuarr fi'ct : and the distance A P is 




Fi- (i7. 



win nee V li is 575.(58 feet; and hence tlie point P can now be 
b'cated from A or B. 

The a/imuth of 1' 1) is determined tlins: 



Tailiiielil (/ P D 



jTD ^•y-^'L 

Vr/ "" 5T5.(;8 + Mi.StN 8.4."')2" 



from wiiich angle d 1' D is found to be 15'.^ 39' 2')", whiili is the 
a>:iniuth of P D. Therefore the length of P D is 



PD 



dD_ 



962.65 feet; 



and tlien tlie field is divided by tlie line P D so that the ana of 
B (• D P is 5 acres. 



PLAXE SUEYEYIXG 



95 



EXAMPLE FOR PRACTICE. 

Divide the field in the above diagram into two parts by an 
assiinied line Q P' parallel to P D so that the azimuth shall be 
45" and the area Q B <• D P' Q shall be 5 acres. 

THE TRUE MERIDIAN. 

In order to ascertain the true mei-idian of a given i)lace, 
several methods may be pursued. The general practice is to use 
the star Polaris at culmination or elongation. This star is on tlie 
meridian, nearly, when a plumb line covers it and the star Zeta, 




Fig. 68. 



the nest to the end of the handle of "The Dipper." See Fig. 68. 

When Polaris is on the meridian, as illustrated in this 

instance, it is said to be at "culmination." This star is often 



PLANE SUKVEYING 



n-ft'iTcd to as the north or ix)le star. It is about 1^^ froui the 
pole, and revolves aroimd the pole once every 23 hours and 5(5 
minutes. Thus it is apparent that it comes on the true meridian 
twice each day. The arrows in the figure indicate the direction of 
the rotation. 

To Determine the True Meridian by the Compass. Wit/i 
Polaris at Eastern or Western Elongation. To determine the 
true meridian by means of the compass, take a plumb-line, and 
attach one tnid of the line to any suitable support situated as far 
above the ground as practicabU', so as to have a clear field of view 
about 20 feet away. A board nailed on a telegraph pole, tree, or 
jKjst at right angles, will suffice for this purpose. The plumb-bob 
may be of any suitable material, of about 5 lbs. in weight, as a brick, 
stone, iron ring, or coupling. It will serve the same purpose, with 
as accurate results, as the most highly polished or carefully manu- 
factured plumb-bob. The plumb-line should be about 25 feet in 
length, deiH'uding upon the latitude of the place, since the altitiide 
of the ix)le above the horizon at any place is equal to the latitude 
of tliat place. 

Illuminate the plumb-line just below its support by means of 
a bull's-eye lantern, lamiJ, or candle, care being taken not to 
obliterate the line from the view of the observer. The best way is 
to screen tlie light, and throw the liglit on the jjbmib-line by 
means of a retlector. 

Next mifasten one of th(i uprights of the conixxiss, and place it 
on a horizontal rest at some convenient point south .of the jjlumb- 
line, say 30 feet in an east or west diri-ction, and in such a 
jxjsition tiiat when viewed througli the pet'ij-siglit. Pohiris will 
apix'ar about two feet bi'low the support of tlie phun])-line. It is 
customary to determine this position by trial the niglit l)efore 
the observation. 

About 25 minutes before the time of elongation, as per table 
on page 130, Ijring the peep-sight into the same line of sight with 
tile plumb-line and tlie star Polaris. Before reaching elongation, 
the star will move away from the plumb-line, to the east for eastern 
elongation, and to the west for w^estern elongation. Hence, by 
moving the p-ep-sight in the jjroper direction that is, east or 
west — the star can be kept on the plumb-line until it appears to 



PLANE SURVEYING 



reuiiiiu stationarj', thus indicating that it has reached its point of 
elongation. The peejj-sight -svill now be seciired in place by a 
clamp or weight, with its exact position marked on the rest. Now 
defer all further operations until the next day. 

The next moi-ning place a slender flag or ranging pole at a 
distance of 200 or 300 feet from the peep-sight, and exactly in line 
with the plumb-line. Next carefully measure this distance, and 
take from the table (page 130) the azimuth of Polaris, corresponding 
to the latitude of the station of observation; find the natural 
tangent of tliis azimuth, and multiply it by the measured distance* 
from the peep-sight to the rod. The product will exj)ress the 
distance to be laid off from the rod, exactly at right angles to the 
direction already determined — that is, .to the west for eastern 
elongation, and to the east for western elongation ; and this jDoint 
with the peep-sight, will define the direction of the meridian with 
sufiicient accuracy for the needs of local siirveyors. 

The position of the pole star may be found by means of the 
two stars ;S and a in the bowl of the ''The Dipper" (Fig. ()8), which 
are called the "pointers" because of their pointing approximately 
to the pole star. 

THE TRANSIT. 

Construction. The transit is used for measuring horizontal 
and vertical angles directly, and for measuring bearings indirectly. 
It consists of a telescope moimted in standards attached to a divided 
horizontal plate, the telescope serving to define accurately the line 
of sight; while the horizontal plate, divided into degrees, minutes, 
and twenty or thirty seconds of arc, makes it ]possible to measure 
small horizontal angles. The instriunent is provided with a tliree- 
or four-screw leveling base, by means of which it is attached to 
the tripod. 

The telesco^De is similar in construction to that of the Wye 
level, but is shorter and of less magnifying piower, a power of from 
24 to 2(3 diameters being about the average for the ordinary transit. 
The eye-piece may be either inverting or erecting, but the former 
is to be preferred. 

Since the principal function of the transit is to secure align- 
ment, the teles copie must be capable of movement in a vertical 



98 PLANE SURVEYING 



plane, ami to that I'lid is sxipijortcd in the standards by a transverse 
axis, jKirmitting the telescope to be "transited." that is. turned 
tlirowgli a complete vertical circl(\ 

For measuring horizontal angles the instrument is arranged 
with an upper and a lower motion, sometimes called the upper and 
the lower "limb." The lower limb is supported by the leveling 
base by means of a hollow conical axis; and into it is titted. in turn, 
the conical axis of the upper lindj. Each limb may be turned 
indejjendently of the other, or they may be clamped together and 
to the leviding base. The lower limb carries the divided circle 
and the iipper limb the vernier. For ordinary inirposes the 
circle is divided to one-half degrees, and reads to single minutes 
by means of tlie vernier. It may also be divided so as to read 
to 20 or )50 si'conds, and occasionally to 10 seconds. The divisions 
of the circle, however, should not be so crowded as to render the 
reading difficult, and the graduations should be properly adjusted 
to tlu» niiignifying jxiwer of the telescope. 

The verniers may be set at right angles to, or parallel with the 
line of sight, or at 30° thereto. With the verniers parallel with 
tiie line of sight — that is to say, directly undi'r the telescope — or 
making an angle of 30° with the line of sight, the observer 
can read the angles without moving from his position, thereby 
avoiding the risk of distiirbing the instrument by walking around 
it. See Fig. ()9. 

For leveling the instrument, tliere are provided two level 
tubes set at right angles to each othi'r. These are shown in thi' 
figure. One of them is attached to the upper ijlate, while the other 
\ty,\y be attached either to the upper plate or to one of the standards. 
On accoTmt of lack of space these level tubes are quite short. 

The four-screw leveling base may consist of two parallel plates 
connected to each other by a one-jialf ball and socket joint, 
or tlie upper plate may be replaced by a ribbed casting. The 
four leveling screws rest in cups upon the lower plate and 
extend through the u])pi'r plate or casting. The leveling base 
is attached to the instriiment proj)er, and the whole is attached 
to the tri^xxl by screwing to a casting firmly attached to the 
legs. The vertical axis is furnished with a hook, to which may 
be attaclied a ]ilund>-liiie for tlie accurate centering of the instrn- 



PLANE SURVEYINa 



90 



uieiit. A shifting cent(^r is also provided, by nieausof which, after 
the iustnimeut has been approximately centered over a stake, it 
may be accurately adjusted by loosening the leveling screws and 
shifting the instrument upon the lower leveling base. See Fig. 09. 




The three-screw leveling base is necessarily larger and differs 
in detail from the four-screw. The upper plate carrying the screws 
is permanently attached to the instrument; and the lower ends of 



lOf) 



PLANE 8UBVEYING 



the screws rest upon the trixjod casting, to which it is attaclicd by 
a singk' center screw fitted with a strong spiral spring that engages 
upon a thread cut uj)on the vertical axis of the instrument. See 



Fi-. 72. 




Fig. 70. 

The four-screw base commends itself from the fact that it can 
quickly be leveled approximately; and, no matter how much the 
threads are worn, the instrument can be brought to a solid bearing. 



PLANE SUEYEYING 



101 



The three-screw base, however, is more easily manipulated, and all 
danger of biudiiig tlie screws and springing the plates is obviated. 
Whichever type of instrument is preferred, the screws should work 




Fig. 71. 

smoothly and evenly, and the pitch should be adjusted to the 
sensitiveness of the bubbles. 

Most transits are fitted with a compass set in the up)ijer plate 



102 



PLANE SUEVEYINfl 




y^-X m 




F,g. 72. 

between the standards: but for city work, triaiigulatioii, etc., the 
compass is dispensed witli. 



PLANE SL^RVEYIXG 



lo:> 



For iiR'asuring vertical angles, the transit is fitted with a 
vertii-al arc or circle divided usually to one-half degrees, and 




Fig. 73. 
reading to single minutes by the vernier. A level tube may also be 
attached to the under side of the telescope; and when this is 



104 PLANE SUEVETmG 

Ijrovided the transit mfiy hn nsed as a leveling instniment. 
A striding level resting iiix)n the standards uuij' also be ijrovided, 
by means of which the instrument can be more accurately leveled 
than by the short levels ii^wn the upper limb. See Fig. 70. 

The telescope should always be jjrovided with stadia wires, 
either fixed or adjustable, though the former are preferable. See 
article on '"Stadia." 

The gradienter screw is a device attached to the clamp of the 
telescoix?, by means of which grades can be established, and 
horizontal distances, vertical angles, and differences of level can be 
ineasureil with great rapidity. See article on " Gradienter" in 
Part TIT. 

Surveyor's Transit. This instrument is the plain transit, 
capable usually of measuring horizontal angles oidy, but occasion- 
ally fitted with a vertical circle or arc for measuring vertical angles. 
S(M- Fig. ra. 

Engineer's Transit. When the instrument is ^jrovided with a 
vertical circle or arc, a level underneath the telescope, with or 
without gradienter screw, it is called the engineer's transit. See 
Fig. 70. 

Tachymeter. This term, meaning rapid measurer, has of 
recent years been applied to an instrument having a level attached 
to the telescope, a vertical arc or circle, and stadia wires. Siich 
an instrument is adapted to the rapid location of x^oints in a 
siirvey, since it is captible of measuring tlie three co-ordinates of a 
]iX)int in space, /. e., the angular co-ordinates of altitude and 
azimuth, and the radius- vector or distance. The compass and 
gradienter are auxiliaries in the measurement of angles; and an 
instrument having tliem in addition to the essential featiires 
mentioned above, is more jxTfectly adapted for tachymetric work. 
See Fig. 71. 

Theodolite. This- term is applied to an instrument so con- 
structed tiiat the telescope will not transit, but, in order to take 
backward sights, the telescoiDC must be lifted oiit of its supports 
and turned end for end. See Fig. 7^!. 

Transit=Theodolite. This name is applied to an instniment 
in wliich the telescope not only can be transited, but also lifted 
out of its supports and turue<l end for end. See Fig. 72. 



PLANE SFKVEYING 105 

Adjustment. When used merely as an angle-measurer, the 
following adjustments should be tested and, if necessary, corrected: 

1st. To ascertahi if the huhhle tides are perpendicular to the 
vertical axis of the instrument. 

To test, attach the instrument to tlie tripod and "set up" firmly 
on solid ground, preferably shaded from sun and wind. Revolve 
the transit u^jon its vertical axis so as to bring the bubble tubes 
parallel to a pair of diagonally opiDosite leveling screws. Bring the 
bubble of one of the txibes to the center by means of these screws. 
Do tlie same with the second bi^bble tube. Adjusting the second 
tube will throw the first one out, but repeat the alternate operations 
until each bubble stands in the center of its tube. Now revolve 
the instrument upon its vertical axis through 180°, and note if the 
bubble of each tube still stands in the center. If so, the tulx>s are 
in adjiistment. 

If the bubble of either tube runs to one end. bring it half-way 
back to the center by raising the opposite end of the tube by means 
of the capstan-headed screw. Kelevel the instrtiment by the 
leveling screws, and again test the tubes. Repeat the operation, 
imtil the bubbles stand in the centers of the tubes in all j)Ositions of 
the instrument. It is advisable to carry out this adjustment as 
precisely as possible, as it will facilitate the remaining adjustments. 
If after several trials, it is found impossible to adjiist the bubbles 
to the centers of the tubes, either the vertical axis is bent or the plates 
are sprung, and the instrument should be sent to the maker for 
correction. If one tube adjusts and the othe:^ does not, the fault is 
in the tube, and a new one shoidd be ordered. 

2d. To maJce the line of collimation revolve in a plane., or, 
in other tvords, to make the line of collimation perpouliciddr to 
the horizontal axis of the telescope' 

To test, having niade the first adjustment, level the instniment 
carefully and clamp the upper limb. Drive a stake into the gromid 
about 300 feet ahead of the instrument, and drive a tack in the 
head of the stake. By means of the lovrer motion revolve the 
instrument on its vertical axis until the intersection of the cross- 
hairs apxjroximately covers the tack. Now clamj) the lower motion, 
and carefully adjust the line of sight uiDon the tack by means of 
the lower tangent screw. Without disturbing either the uiDioer 



KV; PLANE .SUKVEYING 

or the lower limb, transit the telescope, that is, revolve it vertically, 
and sight to a tack in the head of a stake driven into the ground 
abont 3(X) i'ct't IhIiukI \\u' instrument. CarefuU}- adjust the tack 
to the intersection of tiie cross-hairs. Now unclamp the lower 
motion, and revolve the instrument uiDon its vertical axis until the 
intersection of the cross-hairs again covers the tack in the first 
stake. Clamp the lower motion, adjust the line of sigiit carefully 
by means of the tangent screw, again transit tlie telescope, and 
sight in the direction of the second stake. If the intersection 
of tlie cross-liairs falls iipon tlie tack in the second stake, the line 
of collimation is in adjustment. If it does not. it will liave to 
bi' adjusted. 

In Fig. 74, A is the position of tlic instrument, and I^ is tlie 
forward stake. If tlie instrument is in adjustment, the line of 
sight after transiting the telescope and revolving uxjon the vertical 
axis should strike the ix)int B'. If the instrument is not in 



FiK. 74. 

adjustment, the line of sight after transiting the telescope will 
in tlie first instance strike some point as C. Drive a stake at this 
point and carefully center a tack. After revolving the instrument 
uixjii its vertical axis and again transiting the telescope, the line 
of sight will fall at a point C as far on one side of B' as C was 
on the other. Drive a stake at C ' and carefully center it. Carefully 
measure the distance CC; and center a stake at B', half-way 
between the two points. Now, by means of the capstan-headt'd 
screws attached to tlu' diaphragm carrying the cross-hairs, move the 
cross-hairs until their intersection covers the point B", midway 
between B' and C. Now re^x-at the operation of testing the 
adjustment and correcting the position of the line of collimation, 
until the points B and B' are in the same straight line. 

It is necessary only that the line of collimation shall be 
accurati'lv in a<ljustmi'iit : but for con veil iciice in using the transit 



PLANE SURVEYING 101 



as an auglc-nu'asunT it. is desirable that the vertical eross-liair be 
at riglit angles to the horizontal axis of tlu- telescope when the 
instniment is level. 

To ti>st this, set lip (he inslranient at some con\i'nieiit point. 
2(X) or 300 feet from a wall, tree, or other convenient object, npon 
which a point is clearly di-fined by a tack or othenvise. Carefully 
level tile instrument, and cover this point accuratt'ly witli tlie lower 
extremity of the vertical hair. Clamp the horizontal axis of the 
telescope; and by means of the tangent-screw slowly move the 
telescope in a vertical plane, and note if tlie hair continiies to cover 
the point from one extremity to the other. If it does, the hair is in 
its proper position. If not, loosen the diaphragm screws and turn tlie 
diaphragm vertically rmtil the hair covers the i^oint from end to 
end. This adjustment will distiirb the last one and the two nuist 
be tested and corrected alternately until in perfect adjustment. 

If the transit is to be used for leveling, it is necessary tiiat tlie 
horlsdiitdl cross-hair be in the optical center of the objec-t glass. 

To test, set the instriiment up firmly 200 or 300 feet from a 
wall, tree, or other convenient object, and, after leveling, carefully 
center the intersection of the cross-hairs upon a well-defined ijoint. 
Clamp the axis of the telescope, turn the iustriinu'iit upon its 
vertical axis through' 180°, and carefully center a jjoiut upon 
the intersection of the cross-hairs in this new position. Clamp the 
vertical axis, unclamp the telescoxje axis, transit the telescoi)i% and 
carefully center the intersection of the cross-hairs upon the first 
point. Now clamp the telcscoi^e, loosen the vertical axis, and again 
revolve the instrument through ISO'. If the line of collimation 
again strikes the second point, the horizontal cross-hair is in 
adjustment. If not, careftilly center this third point, bisect the 
distance between the second and third ^joints, and move the cross- 
hair diaphragm until the intersection of the cross-hairs covers 
this fourth jioint. This adjustment will disturb the last two, and 
the three must be repeated in succession initil accurately adjusted. 

od. To make the horisontal axis of the telescope perpendtc- 
iihir to the vertical axis of the instrument. 

To test, set up the instrument as explained for the last adjust- 
ment, and, after leveling, center carefully a point at each extremity 
of the horizontal cross-hair. Turn the instrument upon its vertical 



10>S 



PLANE SURVEYING 



axis and transit the telescope, bringing one extremity of the 
liorizontal rross-liair ii[)ou one of the points previously establislied. 
If the otlier extremity coincides with tlie second point, the axis of 
tlie telescope is in adjustment. 

If the axis is out of adjustnunit. thi' method of procedure is 
best illustrated bj- Fig. 75. 

A A ' is tlie line covered between the extremities of the hori- 
zontal wire or hair when the axis of the telescope is in adjustment. 
If it is not in adjustment, the wire will in the first position of the 




telescope cover the line A B, and in the second position the line 
A B ' . Tlierefore bisect the distance B B ' , and raise or lower the 
adjustable end of the telescoixj axis until tiie wire covers A A'. 
Now rejx'at the test, and the correction if necessary. 

4th. To make the axis of the telescope Inihhle txlie parallel to 
the line of colli matioii of the telescope. 

This adjustment should be tested and corrected by the "peg" 
metl)od as follows: Select a piece of comparatively level ground, 
drive a stake, "set up" tlu^ transit over it, and carefully level by 



rffA^7m;'PP7Pmm7?;77m77'7'7'^''^^?'77m 



150' 




the plate, levels. Next drive two stakes into the gromid, one in 
front of the transit and the other at the same distance behind it. 
In Fig. 7<), C is the position of the transit, and A and B are two 
stakes, i>ach loO feet from C. D is a fourth stake behind B and in 
line with it from C. The transit being leveled by the jjlate levels, 
hring the bubble of the telescope tube to the center of the tube, by 
means of the tangent-screw attached to the horizontal axis of the 
telescope. Hold a level ro<l tipon A, ;idjust the target to the 



PLANE SITRVEYINtt lOi) 

horizontcil cross-liair. ami nott' tlir reading. Uuclaiup the lower 
motion, turn the transit upon its vertical axis, ami note the reading 
of a rod held upon B. The difference of the readings of the rod 
held upon the two points will give the true difference of level, no 
matter how mnch the telescope level niaj' bt; out of adjustment. 

Now take up the transit and remove it to the point D. 
Carefidly level the transit by the plate levels, and again bring the 
bubble of the telescope tube to its center. Hold the rod upon the 
poiut B and note its reading. Do the same at the point A, and 
take the difference of the two readings. If tlie telescope level is 
in adjustment, this difference will be the same as found when the 
instrument was over the point C. Otherwise tlic tube is out of 
adjustment and will be corrected as follows: 

Let X represent the difference of level of A and B when tlie 
transit is at C 

Let y represent the. difference of level o[ A and B when tiie 
transit is at D. 

Let z represent the difference between .'■ and //. 

If 1/ is greater tlian ,/■, subtract s from the rod reading upon A 
for the transit at D, and set the target at this new reading. Re- 
volve the telescope upon its horizontal axis, by means of the 
tangent-screw, imtil the horizontal wire accurately bisects the target. 
Now clamp the telescope axis, and bring the bubble to the center 
of the tube by means of the capstan-headed screw at one end 
of the tube. Again hold the rod upon B, and then u^Don A, and 
take the difference of their readings. If this difference now agrees 
with the true difference of elevation of the two points, the adjust- 
ment is complete. Repeat the operation as often as may be 
necessary. 

If 1/ is less than ,/•, add z to the rod reading upon A for the 
transit at D, and set the target at this new reading. Bisect the 
target by the horizontal cross-hair as before, clamp the horizontal 
axis, and bring the bubble to the center of the tube. Test and 
repeat as described before. 

Some transits are provided with an adjustable vernier to the 
vertical circle or arc, which should read 0° when the telescope is 
horizontal. The former adjustment having been completed, the 
vernier can then be readily fixed in place. 



110 PLANE SURYEYING 

Tliu c'l'OSFi-luiir intersection sliinild lie in tlie center of tile field 
ot vision of tlie eye-piece, ;in(l this adjustment may lie made by 
means of tlu- capstan-head screws attached to the eye-piece tube. 

To " set up " the transit. Lift the instrument out of the 
V)OM by placine- (he hands underneath the plates. Avoid lifting it 
by the telescope or the standards. In attaching it to the tripod be 
careful that the threads engage properly, and screw it down firndy. 
Examine the tripod legs, and see that they are projjerly attached 
to till! tripod head, neither too tight nor too loose. See tliat tlie 
tri^xxl shoes are tiglit, and, before taking up the instrument, 
lightl}' clamp all the movable parts to prevent unnecessary wear 
and straining. Carry the instrument in the most convenient way, 
taking care not to hit it against trees, lamp-posts, doors, etc. 

To center the transit over a stake, rest one leg of the tripod 
upon the ground, and, grasping the other legs, pull the instrument 
in the jn'oper direction to cover the stake. Now attach tlie iilunib- 
line, and after bringing it to rest as close to the top of the stake 
as possible, note if tiie point is directly over the point in the 
stake. ]f it is not too far off the center, it may be brought 
closer by forcing the opposite leg into the ground or by a further 
spreading of the legs. After the instrument has lieeu approxi- 
mately centered, it may be accurately adjusted liy means of the 
shifting liead. The operation of "setti'ng up" is difficult of 
description, and facility can be attained onlj' by practice. Avoid 
having the plates too much out of- l(>vel, as this will result in 
unnecessary straining of the leveling screws and plates. 

Having centered the instrument over the stake, level it up by 
the levels ui)on th(^ horizontal j^late. To do this, turn the 
instrument upon its vertical axis until the bubble tubes are 
parallel to a pair of diagonally opposite plate-screws. Now, as 
you stand facing the instrument, grasp the screws between the 
thumb and forefinger, and turn the thumb of the left hand in the 
direction the bubble must move. Turn both thumbs in, or both 
thumbs out. Adjusting one tubi' will disturb tlu' other, but adjust 
each alternately until tlie bubble of each remains in the center. 

To measure a horizontal angle by means of the transit. 
Set up the transit over tlie point (', Fig. 77. Set the verniers 



PLANE SITiVEYINCI 



111 




Fit;. 



to re;id 0°, and clanip the iix^per limb. Now vevolve the transit 
upon its vertical axis by the lower motion, and sight to A. ClauiiJ 
the lower motion, and acciirately adjnst the intersection of the 
cross-hairs to tlie poiut by nu'ans of thi' 
lower tangent-screw. Now unclanipthe npper 
linil), and turn it Tipon its tipper vi'rtical 
axis to tlie point B. Clamp tlie nx^per limb 
and adjust the line of siglit by tlu> upper 
tangent-screw. The angle will now be found 
recorded upon the horizontal circli'. If it beconu'S nect'ssary to 
repeat the angh-, looseu the lower motion, and, without disturbing 
the up^K-r plate, tuni tlie instnmient back to the point A. Next 
clamp tlie lower motion, looseu the upper, a i id turn tlie telescope 
to the xioiiit B. The sum of the two measured angles will now be 
found recorded upon tlie horizontal circh-. Repeat as often as' 
necessary, and divide the total liorizontal angle by the immber of 
repetitions for the probable value of tiie angh; A B C. 

The oixu'ation of laying off a certain angle is essentially the 
same as the preceding, except that after the point A has been 
centered and the reipiired angli' laid otf upon tlii; horizontal circle, 
the tack in tlie stake B must be moved back and forth until it is 
accurately centered at the intersection of tiie cross-hairs. 

To survey a series of lines by means of the transit. "Set up" 
the transit over the poiut A, Fig. 78, and make the verniers read 
0^. Have the north end of the plate ahead ^ tliat is, in the 
direction of the survey. If a true meridian line has pyreviously been 
laid out, tlie declinatiou of the ^ 
needle may be detenu iiied from it . 
Withoirt disturbing the upper 
plate, turn the transit upon its 
lower motion, and center upon B. 
Let the needle down uxjou its 
pivot, and as soon as it has come 
to rest take the bearing of the line 
AB. To measure the length of the line, hold one end of the tape or 
cliain diri'ctly u.nder the ijoint of the plumb-bob, and send the head 
man in the direction of B. As he reaches the end of his tape, 
Ijlace him accurately in line by the vertical hair. For this purpose 



30' 



FiK. 



;si°o 



v' -ss'o' 



112 



PLANE SURVEYING 



the telescoixi should be turned in a vertical ijlaiie to bring the 
intersection as closely as jjossible to the tojj of the stake. Now 
rei^eat this oijeratiou until the iJoint B is reached. Move the 
transit to the ix>int B, and set it uj) as before with the north end of 
the i)late ahead. Transit the telescope, and examine the verniers 
to see if they reiid 0°. By means of the lower motion, center upon 
A, lowiT the needle, and take the bearing. Now clamp the lower 
motion, transit tlie telescope, and revolve the upper plate so the 
telescope iK)ints to C. Kead the angh-, which is that between A B 
proiluced and B C. Also read the Ix'aring from the compass. Now 
measure B C as exphiined before, take up the instrument, and set 
it wp at the jwint C Continiie thus until the series of lines have 
been surveyed. 

The angles measured are those indicated by the dotted lines 
(Fig. 78), and are called deflection angles. 

It is desirable in work of tliis character to calculate the bearing 
or azimuth of a line from the deflection angle, and to clieck the 
result by the compass. Referring to the figure, the records of the 
survey will be kept as follows, using the left-hand page of the 
transit or field book and starting from the bottom of tlie page: 



7 


0.") 


") 


:Kt 


2 


- !M) 








DISTANCE. 



DEFLECTIOK. 



COMPASS. 



DEDUCED 
BEARINGS. 



27,", 


o2 0' 


S52'45' E ■ 


S52=30'E 


•j(k> r,r 0' 




XT.'V I.-)' E 


N 7.5-= .■»• E 


■>¥) 


31" 30' 


Srvi'4.T' E 


S53 30' E 


290 




S85=E 





It is not absolutely necessary iii the method described above, 
that the verniers slumld be set to rejid 0' before aligning the 
instrument, provided tliat tlie verniers are read before turning otf 
the angle. For instance, if the verniers read 40° 15' after the 
instrument is set up over a stake, and after sighting along a certain 
line, read G0° 15', the angle between the two lines is the difference 
of the reading of the verniers, or 20°. 

As already explained under "the compass," tlie dircctiiju of a 
line may be given by its aziiiinlh. If azimntlis are computed from 



PLANE SUEYEYING 



113 



the nortli to the riglit through i3()0"\ tlie azimutlio for the preceding 
case will be as follo^vs, as illustrated by the diagram: 

Since the bearing of the first line A B (Fig. 79), given by 
the compass, is S 85° E, its azimuth will evidently be the difference 
between 180° and 85°, or 95°. Since the second line B C 
deflects to the right by 31° 30', its azimuth will evidently be th e 
sum of tlie angles 95° and 31° 30', or 12*5° ."'O'. Since the third 
line C D deflects to the left 51° 0', its azimutli will be the differ- 
ence of the angles 12G° 30' and 51° 0', or 75° 30'. The fourth 
line T> E deflects to the right 52° 0', and therefore its azimuth will 
M. the smn of the an-des 75° 30' and 52° 0', = 127° 30'. 




The same diagram may serve to illustrate the method of 
deducing the bearings of a series of lines from the deflection 
angles. Since the bearing of the first Hue as given by the compass 
is S 85° E, and the second line deflects to the right 31° 30', it is 
evident that this second line decreases its easting by that amoiuit, 
so that its bearing will be the difference between 85° and 31° 30', 
= S 53° 30' E. Since the third com-se deflects to the left by 51° 
0', its bearing to the east will be increased by this amount, but will 
pass into the northeast quadrant by 11° 30', making its bearing 
90°— 14° 80', = N 75° 30' E. The fourth course deflects to the 
right 52° 0', retimiing to the southeast quadrant by 37° 30', 
making its bearing 90°- 37° 30', or S 52° 30' E, 



114 



PLANE SURVEYING 



Traversing. This i« a iiicthoil of observing ;iiid recording the 
directions of a series of lines of a survey, so as to read off, upon 
the horizontal circle, the angles that the lines make with some 
other line of the; snrvey, which may be either a tnie meridian or 
some line adopted as a meridian for that snrvey. 

Before starting ont upon a tra\-erse, it is best to la^' out upon 
the ground a true meridian, eitlier from observations on Polaris or 
by uu'ans of the '"Solar transit." as will be explained later on. This 
lino should bt; 'M) or 4(X) feet in lengtli, clearly defined by stakes 
carefully centered, one of the stakes jjreferably being the first 
station of the survey. Tlie transit can uow be set over this stake, 
and tlie line of sight carefully centered upon the second stake by 
means of the lower motion, tlie verniers first ha\'ing been set to 
read 0°. Tlie subsequent oiJeratious can best be illustrated by a 
diairrain. 




C9 -CccS It's — 



FiL'. 80. 



First lay ont a meridian tlirougli station 1 (Fig. 8 )|, and 
define it l)y a stake driven BUG or 400 fi'i't away towards N. Both 
of these stakes shonld be carefully "witnessed," that they may be 
recovered at any time. To begin the survey, carefully center the 
transit over station 1, with verniers set to atTo; turn tlie instrument 
uijon its lowuT motion until tlie line of siglit approximately 
i-overs till' stakes at the north end of thi; meridian, and carefully 
center it by tlie lower tangent-screw; lower the compass needle (i 
there is one), and note aud record the magnetic declination. Next, 
with the lower motion securely c-Limpcd. unclamp tlie ii})pi'r iiiotioii. 
and revolve tlu! ujjper plate in tlic dii'cction of statirm -2. ("lamp 
the upiier motion, and carefully center the line of sight by the 



PLAXE SURVEYING 115 

upper tciiigent-st'i\'\y. Note and reeoij the angle upou the plate, 
which will be the azimntli of the line 1 2. Measxire the dislauee 
from 1 to 2, aud note and record tlu> compass bearing as a check. 

Now, with the iip^jer motion securely clami)ed, remove the 
transit to station 2; and carefully center it over t1ii> stake with the 
north end of the plate aliead, that is, in tlie direction from 1 to 2. 
Transit the teleseoxx', unclauip the lowi'r motion, and bring the 
line of siglit to cover station 1. Oarefidly center it by tlie low(>r 
tangent-screw. Clamp the lower motion, transit tlie telescope, 
unclauip the upper motion, and revolve the upper plate luitil the 
line of sight falls upon station 3, carefully centering it by the 
ui^per tangent-screw. Read and record the plate angle, which will 
be the aziuurth of the line 2 3. Measure the distance from 2 to 3, 
and read the bearing of the needle for a check. 

Now see that the upjjer plate is securely clamped, move the 
instrument to station 3, and proceed as before; and so on through- 
out the traverse. 

After moving the transit from one station to another, the 
horizontal circle should be read, to see tliat the plates have not 
slipped as may occasionally happen, i^articularly when the clamps 
are worn or when the instrument-man inadvertently loosens the 
wrong screw. For this reason, if for no other, it woidd seem safer 
to set the verniers at zero at each station. nieasui-e tlu^ deflection 
angles, and calculate the aziuinths. 

In carrying out an extended traverse, it is desirable to lay out 
a true meridian from tim(> to time, to cheek the azimuths and the 
declination of the net'dle. 

For city work, the engineer slioukl lay out a true meridian 300 
or 400 feet long, and mark the extremities of the line by ijerma- 
ueut monuments set iu the ground and carefully XJi'otected from 
disturbance. To do this, in some convenient place xjermitting an 
unobstructed line, of siglit, drive a large stake, aud mark its center 
by a hollow-headed tack. Center the transit caref\dly over this 
point, and prncicd ti > lay out a true meridian, preferably with the 
solar attai-hment. Mark the direction of this line by a second 
stake carefully centered by a tack as befori\ Now, about 25 feet 
from the first stake, aud in line with it and the second stake, 
excavate a hole in the ground about three feet in diameter and five 



lir, PLANE SUKVEYIXG 

ffet det'p, or deei> enough to be below the frost line. Next build 
a foundation of concrete aboiit two feet square and three feet deep. 
Before this has "set", insert in it a cut-stone post about nine inches 
square .at its lower end and of such length that its top will come 
just below the siirface of the ground, and having set into its top a 
copper bolt about | inch by 4 inches. The post may be centered 
in the concrete by means of the transit, and should be set "ijlumb". 

Now locate and build a second monimient in line witli the 
second stake and a few feet from it. After the concrete has set 
firmly, again set the transit carefully over the center of the first 
stake, and accurately align it by the tack in the second stake. Now 
"lilunge" (reverse) the telescope, and carefully center a jaoint in the 
top of the coi^ix^r bolt; mark this point with a steel punch. In the 
same way center a ix)int in the top of the bolt of the second monu- 
ment. The monuments may be protected by enclosing them in cast- 
iron valve-boxes witli covers. Either one or both of these monuments 
may be used as "standard" bench-marks from which all the levels 
and grades may be ascertained. For this purpose a city datum 
may be assumed, or better, the bench-mark may be connected by a 
line of levels with a bench-mark of the U. S. Coast and Geodetic 
Survey, or, if such is not available, with a bench-mark of the 
nearest railroad. 

The following article uijon traversing describes a method of 
using the transit somewhat different in detail from the preceding 
artic-le. It offers a concrete example, and ilhistrates the method of 
recording the notes of a survey. 

TRAVERSING. 

The term " traversed,"' which was originally associated with 
navigation, is commonly used by surveyors to define a series of 
lines whose lengths and relative directions are known. Fig. 81 
shows a traverse T P R S W X. It is required to locate a point X 
from T, which cannot be done directly on account of dense mider- 
brush, woods, and other natural obstriictions. Some other means 
must therefore be provided, which may be in the form of a series 
of short cords, as T P, P E, R S, S W, and W X. It sometimes 
occurs that while there may be no obstruction between the i)oints, 
the distfuice from one ])oint to the other is of siich a length that 



PLANE SURVEYING 



117 



it is impossiblo to sccim- an iicciiiato line of sight. Several 
points, therefore, nmstbo estiiblisliud in order to reaeli the desired 
spring X. Traversing, as will be evidi-nt, is particixlarlj- a^jplicable 
to the STirvey of long aiid circxiitons routes throngh territory 
presenting natural obstructions to long sights. It is almost 
universally adojjted in filling in the details of majjs based on a 
system of triangidation. As examples of traversing, may be 
mentioned the survey of highwaj-s, railroads, river banks, shores 
of lakes, and property bomidaries. 

In the United States government sxu'vey, when a traverse is 
run to mark the divisions between private estates and bodies of 
water retained as public property, it is called a meander line. 

The transit is particularly adapted to traversing, and is so set 
at each station tliat tlie azimuth 
of each line can be directlj' read. 
If the survey is made in a 
locality where no system of latitude 
and longitude has been established, 
the magnetic meridian may be 
taken as the meridian of an azi- 
muth. At the first station the 
vernier is set at zero; and by means 
of tlie lower motion the instrument 
is turned so that the north end of 
the needle points to the north on 
the compass limb. The lower plate 
being clamiDed, the upper one is 
unclamjjed. Now, if a sight be taken at any object, the reading 
on the vernier will be the azimuth corresponding to the bearing of 
that object. The last sight reading taken at the first station, is 
towards the second station of the traverse line. 

The instrument is then placed over the second station, and the 
vernier set at the back azimrith of the first station. The azimuth 
of any line from the second station will now correspond with its 
bearing as before. The readings of the needle are regarded as a 
rough check on the azimuth, with which they should agree to the 
nearest eighth of a degree. For example, at station A (Fig. 81) 
let the bearing of AB be N 74° 15' E, and let its azimuth be 74° 




118 



PLANE SUEVEYmd 



15'. Ou placing tlie iiistrumeat at B, li't tlie vernier be set at 
254" 15', a sight taken on A, and the lowt^r plate clamped. The 
azimuth of BC will be 143° 02', the vernier being set at 323° 02' 
on arriving at C. Tlie limb is x>laeed in the iwoper position by 
sighting back to B. The telescope is not reversed during anj' part of 
the work. At each of the stations, sights may be taken to surround- 
ing objects; and if the distance to an object is measiired, this, 
together with its azimuth, locates it with respect to the station. 
The field notes are kept as follows regarding the above stations: 



BEARING. 


AZIMUTH. 


DISTANCE. 


OBJECT SIGHTS. 


Station B 








S 74° 15' W 


254° 15' 


528.3 


Station A. 




.325 42 


2,50 


Large pine tree. 




196 24 




N. E. corner of 

John Doe's house. 




194 10 




S. E. corner same house. 


S 37' (X)' K 


143 02 


490.7 


Statipn 0. 


Station C 








N 37° 0.5' W 


32.3 02 


490.7 


Station B. 




280 13 




N. E. corner John Doe's 
house. 




276 15 




S. E. corner same house. 




104 07 


98.5 


Fence corner. 


S 42" 45' E 


1.35 15 


.504.6 


Station D. 



JA- 



owriUNG [ — ] 

BARN 




» Fig. 82. 

The field notes with offsets are taken from the traverse line, 
and are best kept as in Figs. 82 and 83, the b(>aring of a line being 
written ujion one side of it, and tlie azimuth upon the other side. 



PLANE SURVEYING 



119 



Where no otfsets iue taken, flie fieltl notes are k(>pt as above. Tlie 
large pine tree is located by azimuth, and the distance at station 
B, as is also the fence comer at station C. The housi' of John Doe, 

however, is located by azi- 
muth taken from B and C, 
tlie line BC forming the 
base, from which its dis- 
tance from eitlier end can 
be computed. Wliere a 
traverse is nu i, a check must 
always be emi:)loyed so as 
to ascertain the acciiracy 
of the work. In a closed 
traverse, such as one around 
the bcundari(>s of a farm, 
this is easily obtained, since 
the sum of the northings 
equals the sum of the south- 
ings, and the simi of the 
eastings equals the sum of 
the westings. In Fig. 81, 




Fijj. 3.3. 



the traverre C N S W X F G, which begins at C and ends at G, 

is checked in the field on arriving at G; for the azimuth of FG must 

agree with that previously obtained: 

also in computation the differences 

of latitivh^ and longitude between B 

and C must equal those derived frorr 

the main polygon. It should be 

remarked that the object in taking 

the bearing is to check gross 

error in the azimuth during the 

progress of the work. If the true 

meridian has been established m the 

neighborhood of a survey, the azi- i^'ig- S- 

muth sliould be taker- from it instead of the magnet^'c meridian. 




120 



PLANE SURVEYTXn 



EXAMPLE FOR PRACTICE. 

Coinpiitt' from the above notes the length of the west side of 
John Doe's honse Obtain the same result withoiit compntations 
by plottiiig tlie distance. 



THE STADIA. 

Attached to tlie diaphragm carrj'ing the horizontal and vertical 
hairs, are two anxiliary horizontal hairs called "stadia"' hairs or 
wires. These hairs may be either fixed in position or adjnstable 




Fi^r. sr,. 

bnt the fixed hairs are the l)i>tter for field nse and cost much less. 
See Fig. 84. .Vny instrument-maker will eipiip a level or a 
transit with eitlier fixed or adjustable stadia wires, and they should 
b(> included in every outfit. 

The Stadia is used for measuring horizontal distances and 
differences of elevation, without the use of chain or tape or other 
ap])aratus except tlie leveling rod or a, si>ecially graduated stadia 







c, ^^„^ 


S 






Sa 




C J\^^ ^^1=:^==^^^^^^^^''^^ 




C) 


3^^=--^ 


So 






^-O^ 






^--J 


D ^~'^~~-~ 


s, 



FiR. so. 

rod. It is bast^l upon th(> principle of the similarity of triangles. 
Thus, if tlie stadia hairs are spaced so as to intercept one foot u^jon 
a rotl held at a distance of one hundred feet, the rod intercept 
for any other distance will be in direct proportion to the first. 
See Fig. 85. 



PLANE SURVEYING 



121 



Uiifortuiiatfly the construction of tlie telescox3e of an engineer- 
ing instrnuient moilifii'S the above simple statement, anil a formula. 
for tlie \ise of the stadia will now be deduced. 

Let O in Fig. 86 be the optical center of the object-glass of 
tlie telescope. This point may be assumed at the center of the 
h'Ms, and the error involved in such assumption is inappreciable 
■lad may be neglected. 

Li't SSi be a ijortion of the stadia rod covered by the stadia 
liairs CCi. From-C and Ci draw the lines CSi andCiS through the 
optical center of the object-glass. Upon looking through the eye- 
piece of the telescope, C will be seen a"- at Si and Ci as at S. 




Pit;. 87. 



Call ?' tho distance between the stadia hairs, s tlie intercept 
upon the rod, _/'' the distance from O to tlie wires, and (/ the 
distance of the rod from O. 

Tlie triangles COCi and SOtii are similar, and therefore w<' have 
the xiroportiou 

i: s :: /' : a 
f's 



therefore c? 



(») 



But/' varies with d. That is to say, if the rod were to be 
moved closer to the instrument, as at C2D, the lens would be moved 
farther from the wires, or the wires from the lens, and in either 
case the wire interval would intercept a shorter space upon the rod, 

as 828:1. The ratio 



-^—. — , or its equal — , will therefore vary 



for each position of the rod. But however they vary, we have from 
a well-known principle of optics : 



122 PLANE SURVEYING 



in which _/' is the principal focal distance of the lens, and /" and 
d are any pair of conjugate focal distances. Substituting the 

value of . , from (1) in (2), there results the equation 
d = {' s + /. (3) 

Equation 8 gives the distance of the rod from the lens. 
We can establish some very important relations: 
lu Fig. 87 lay off OF' = OF = principal focal distance of 

lens =y. 

and Cibeing the stadia wires, draw C D and Ci E parallel to 

the axis of the lens, and through F' draw D Si and E S; then will 

S Sj = the intercept upon the rod. 

The distance of the rod from the jioint F' is 

d' = d -/=( -^ * +/) -/ = {-*. 

From the similarity of the triangles EF'O, SF'B and SsF'B', we 
have: 

F'O : OE :: F'B : BS :: F'B' : B'S,. 
Therefore the points S, Si, F', and E lie in the same straight 
line; and therefore, wherever the cross-hairs are situated, or, more 
strictly, whatever may be tlie position of the lens, the visual lines 
defined by the stadia wires will intercept the elements of the; cone 
of light defined by SF' Si. 

All distances must be measured from the center of the 

instrument; and therefore to the expression d = ' . s -\- f must be 

added a quantity that will represent the distance from tlie center 
of the k'lis to tlie plumb-line. This cpiantity is variable, of course, 
but an average value is usually taken. Call this quantity c. The 
(quantity /'may be found by focusing the instrument on a star, and 
measuring the distance from the center of the lens to the cross- 
hairs. We can therefore determine the quantity /'+ c. This, 
however, is usually supplied by the instrument-maker, and with 
greater precision. 



PLANE SUEVEYTNG 12H 

The couipk'te equation, therefore, for any distance measured 
with the stadia, is: 

d=-t.v + C/'+r) (4> 

If, then, upon level ground we lay otf the distance/' + c in 
front of the pluuib-line, drive a stake, measure from this stake a 
distance of 100 or 200 feet, or any other convenient distance, and 

note the rod intercept, then in the formula (/' =' . «. d' and *■ are 
measured, and we can determine the ratio'. ; or, if /'has been 

previously determined, we can determine the value / or the distance 
between the cross-hairs. 

The ratio --being known, distances can be foiind from. 

equation 4. It is usually most convenit'ut to make this ratio 100, 
so that at a distance of 100 feet the wires will intercept one foot 
upon the rod. 

The rod may be either an ordinary leveling rod, or a stadia 
rod divided specially for the telescope and wires. When the rod is 
specially graduated, it may be in either one of two ways. Either 
it may be graduated so as to give the distance from F', in which 
case the qiiantity /'+ t; will have to be added in each instance; 
or it may be graduated to give distances from the center directly. 

If the rod is to be gradiiated sxjecially, proceed as follows : 

Carefully level the line of collimation of the telescope, and lay 
off from the plumb-line the distance /' + r. From the point 
thus established measure otf any convenient distance, as 500 feet, 
on a horizontal jjlane. Set up the rod, not yet graduated, at this 
point, and hold it carefully perpendicular to the line of sight from 
the telescope. This can best be done by means of a plumb-line. 
Be careful to eliminate all parallactic motion of the wires on the 
rod, when the eye is moved up and down before the eye-piece. 

Mark on the rod verj' carefully tlie apparent j)lace of the lower 
wire. This should be about one-quarter the length of the rod from 
one end if the horizontal distance first laid off is about one-kalf 
the greatest distance for which the rod can be used. The middle 
wire will then be at about the middle of the rod, and the upper 
one at about one-quarter the length of the rod from the other end. 



124 



PLANE SURVEYING 



Mark the latter point carefully. Tlie wire interval for a space of 
500 feet from F' has thus been found. One-fifth of this space will 
be the wire intercept at a distance of 100 te(^t; twice the space, 
the intercept for 1,000 feet; and so on. The intermediate spaces 
can thus be graduated. It miist not be forgotten that in using 
the rod til us gra<luated, the quantity /'+ '' must be added to tlu» 
distance indicated by the rod, to reduce the distance to the center 
of the instrument. 

If till' rod is to be graduated to give distances from tlie center 
of the instrument directly, procei'd as before, marking the spaces 
uiion the rod corresponding to the distances irti-asunHl upon the 
ground. The (luaiitily /' -{- e will not now have to lie adde(l 




to the distances given by the rod; but I'qr every point other than 
that for which the rod is graduated, the distance will be in error 
by some fractional part oi f -\- r. The reason for this will he 
apparent by referring to Fig. !S7. If the distanci' is less than 
that for^vhicli the rod was graduated, the rod readings will indicate 
too small a distance; and for a distance greater than tlu^ standard, 
the rotl ri'adings will indicate a distance too great. It is therefore 
more exact to mark the wire interval at 100 feet, 200 feet, ami so on 
through the length of the rod. Each space thus determined can 
be divided up as desired; and the error involved in any reading 
will then be much smaller than if the rod were graduated for a 
single standard distance only. 



PLANE SURVEYING 12.-) 

Thus far the rod has been assiimed as lield iJerpeiidicular to 
the line of sight, which of course will always be the case when 
using the stadia in tlie leveling instrument. The stadia, however, 
finds its greatest usefulness in connection with the transit, when 
the line of sight is seldom horizontal. If, at the same time tlie 
rod intercept is read, the vertical angle is noted, differences of 
elevation may be determined, as well as the distances. 

A formula will now be dediiced for reducing inclined readings 
to the horizontal, and for determining differences of elevation, the 
rcKl being held vertical. 

In Fig. 88, let the angle of inclination of the line of siglit to 
the horizontal plane be called "B C N = F B D = I. This angle 
will be measured upon the vertical cii'cle of the transit. If the 
rod be held perpendicular to-^;he line of sight, the intercept upon 
the rod = D E = a-. Represent the rod intercejjt when the rod is 
ht'ld vertical by *• ' . Now since the angle P D B = 90° nearly, 

D E = F G cos I, or « =.s' cos I. But C B = ^-s + (/+ r) = 

f 

--. s' cos I + (/ + v). Therefore the horizontal distance to tlic rod 

= C B cos I = J,-s ' cos- ! + (/■+ <:) cos I = C N. The vertical 
distances of the jjoint B above the horizontal plane througli tlic 
axis of tlie telescope = B N = C B sin I = -. s' cos I §in I + 

(./■ + c) sin I == -J ^t.s ' sin 2 I + (/ + c) sin I. 

For vertical angles less than S'' the qiiantity (/'+ '•) sin I is 
less than 0.1 {f-\- c) and may be neglected. 

The Use of the Stadia in the Field. In using the stadia wires 
in level country, no special iustructions are necessary, as the line of 
sight is at all times horizontal. Over very uneven ground, the 
use of the level and stadia is very limited. However, there arc 
often conditions in which the stadia wires in a leveling instrument 
'are a very great convenience. The range of the instrument may 
sometimes be increased by using the center wire together with one 
of the stadia wires, but the instrument should be carefully tested 
to ascertain if the stadia wii'cs are equally Spaced with reference to 
the middle wire. 



ISfi PLANE SUKVEYIKG 

For extended surveys over imeveu country, the transit aud 
stadia are particularly adapted, and especially for filling in details 
of an extended toi)ogniphical survey. The saving of time and 
expense are imiwrtant ek-nients in favor of the transit and stadia 
as compared with the transit and tape; and with a little practice 
and attention to details the results should be fully as acciirate. 
Certainly, when an engineer must depend uix)n unskilled help to 
carry the tajx?, there can be no choice as to which to iise. 

For use with the stadia, the transit should be i»ovided with a 
complete vertical circle, rt>ading to minutes at least; and a level 
tube should be attached to the telescope. The eye-piece sliould be 
inverting. Before starting out upon a survej', the transit sliould 
be carefully tested and corrected through all of its adjustments. 
The field operations are tlu-h as follows: 

Set up the instnxnunt over a principal station of the survey, 
and level it carefully. If a solar attachment is available, it will be 
desirable to lay out a true meridian, from which the declination of 

the needle may be determined. 
Now determine the height of the 
cross-hairs by holding the stadia 
Tcn\ close to the side of the 
instrument, and noting the height 
of tile center of the horizontal 
axis of the telescope. Locate 
Fi^. 80. the second station carefully, and 

turn the ti'lescope upon thi' horizontal axis xiiitil the center wire 
cuts the division nimn tlie roil (held upon the ground) representing 
the height of tlie axis of the instrument above the groiind at the 
first station. Now determine tlie azimuth of the line conm'cting 
the two stations, read the vertical angle of the telesco|)e, and 
determine the nxl intercept. Enter these items in the field book 
and proceed to take observations iijion sub-stations (called "side- 
shots'"). 

The same program is to be reix^ated for each case, excejjt that 
ihe side-siiots may or may not be taken upon points indicated by 
stakes. Tlie priiiciijjil stations of a stadia survey should be 
permanent ; tlie stakes sliould be driven, and "witnessed"' so as to 
be easily recovered. 




PLAXE SUEVETING 



-127 



Having now located all the necessarj- uoints from the first 
station, remove the instrument to the second station, and set it up 
with the north end of the plate in the direction of the sm-vey. 
Having carefully leveled the instrmnent, determine the height 
of its axis as before, and send the rod back to the first station. 
Transit the telescope, and sight upon the rod as before, Eead 
vertical angle and stadia rod, and determine azimuth, and these 
will serve to check the former determinations. 

In moving from one station to another it is advisable to set 
the scale of the horizontal circle to zero. Transit the telescope 
again and locate the nest station; and soon throughout the survey. 

The principal stations of a stadia survey may have been 
located by a previous triangidation, in which case it will probably 
be necessary to locate intermediate stations as the siir\'ey 
progresses. Or all of the stations may^be located during the 
progress of the survey. The courses connecting the jprincipal 
stations form the '"backbone" of the siu^^ej-, and the azimuths 
and distances should be checked at every opportunity. 

In keeping the field notes, represent the princii^al stations by 
triangles, as ^i ^c^a ^^s, etc.: and the secondary stations by circles, 
as 01 ©2 Gs, etc. 

Below wiU be found an examj)le of the method of keeijing 
notes. Use the right-hand ixige for sketches, or for such additional 
notes as may be necessary. 



H. I. 5.1.5 



d 

e 



1 

2 
3 
4 
5 
1 

e 



A 



238 

265 

236 

237 

261 

42.5 

H. I. 47.3 

245 

.300 

.345 



ELEV. 100. 



VERT. I DFFFER- 
ANGLE. I ENCE. 



88^ .38' W 

57 41 W 

49' 3 W 

32= 58- W 

0' 13' W 

44= 13 E 

1.35 41 E 

200= 23 W 

204= 2' W 

203' 12 ^V 



.57 


- 3.9 


-- 58' 


— 4.6 


— .38 


- 4.6 


— 1= 7 


^ 4.6 


— 1 3 


— 4.6 


— 0' 6 


-- 7.5 


-1°.57 


- 8.3 


-1 .31 


- 7.9 


- 58' 


+ 5.8 



96.1 
95.4 
95.4 
95.4 
95.4 
99.25 

107.6 
101.2 
105.1 



Stadia Rods. Telemeter or stadia rods are made of clear white 
pine well seasoned, about | of an inch thick, from 4 to -Li inches 



128 



PLANE SURVEYING 



wide, and from 10 to K) feet long. They are protected by a metal 
shoe to keep the lower end from being battered or split. The rod 
is stiifened by having a piece 2^ inches wide along its back. 
Generally a stadia rod is hinged at the center for greater con- 
venience in transportation, and at the same time it is provided 
with a bolt on the back to protect the graduation and to hold it in 
position when in use. 

A self-reading level rod may be used for distances if the wires 
are adjustable (see Figs. iSUandyil, or if the wire interval has 










Kit;, ill. 
been determined in standard lUiits. The rods 
tised in connection with tliis grade of work differ 
from those employed in ordinary leveling. 
Tiiose with graduations have the inner surface 
ivcessed to [jrotect the graduated surface, and 
Fig. 90. .,re painted white with tlie scaU- in black. The ^'f^- "-• 
forms of graduation are diffenmt on ditferi'ut rods. In sonn', the 
unit of measure is the meter, whik' others have the foot, as will be 
di'scrilx'd later. When telemeters are in use, they are oix'U, laid 
Hat, and held securely in line by the brass clip (or bolt) above 
referred to. Tliey are sometimes provided with a target. 

In order to have the rod held in a ])erfectly vei-ti<-al jjositioii. 
a small telesco^X' is sometimes attaclied to its side, by means of 




COAST SURVEY PARTY STARTING TO WORK FROM A TRIANGULATION STATION 

The topogi'apher and his assistant are ad.iustiug the instrument under the "signal;" th€ 
instrument man is at his never-ending tasli of putting needle-points on pencils; one of the 
rodmen (with telemeter rod) is waiting for instructions to set out, and the other is picking 
up other "signals" with the glasses. 



PLANE SURVEYIN(t 



12it 



4 
< 



X 

♦ 

♦ 

♦ 

♦ 



e:i 



I 



E 



M 

< 



El 

9 = 



^i 






M»| 



A, B and C—V. S. Coast Survey 



C D 

D— U. S. Lake Suirey. 

Fig. 93. 



K— U. S. Engiueers. 



i:?0 PLANE SURVEYING 



which the rodmau can tfU whether the rod is in a vertical i^lane. 

Figs. 90 and 93, D, show two tyijes of gradiiations suitable 
where the meter is the xuiit. Fig. 93, D, has for many years been 
used by the United States Coast and Geodetic Survey as well as 
by the United States Lake Survey. The angles of graduation divide 
the rod into two centimeter intervals. Fig. 90 shows the rod used 
on the survey of the Mexican border. The graduation is apiDarent, 
and no further exi^lauatiou need here be given. 

Figs; 92 and 93, C, are types suitable where the foot is tlie iniit. 
In Fig. 92 the width comprised between the ends of the points divide 
into five ecpial parts, tlie vertical black lines taking vip two of these 
differences. The diagonal then gives one hundredth of a foot, and 
jjermits ri-adings direct to single feet. Fig. 91 shows a plain 
ro<l without scale, and tlic unit is the foot. Classes A, B, C. D and 
E, Fig. 9;?. belong to tlu; respective surveys as indicated. 



PLANE SUKVEYING 



131 



TIME OF ELOXGATIOX AXD CULMIXATION OF POLARIS. 



DATE IN 1899. 


, E.VST 
ELO.NG.\TIO.N. 


UPPER 
CULMINATION. 


WEST 
ELONGATION. 


LOWER 
CCLMIN.4TION 






h. 


Ul. 


h. 


111. 


h. 


111. 


h. 


111. 


.Tiiiiuaiv 


1 





41.9 


G 


.•!ti.7 


12 


.•n.5 


18 


31 . 7 




1.') 


i'i 


42.7 


.5 


41.7 


11 


3(i.2 


n 


:3SI.I 


Fi'lnuiiiv 


1 


22 


.•15.5 


4 


.34.3 


10 


29.1 


16 


:32.3 




1.-5 


21 


40.. T 


3 


.39.0 


9 


.3:3.9 


15 


:37.0 


March 


1 


20 


45.1 


•> 


43.6 


8 


38.6 


14 


41. S 




lo 


19 


.50.0 


1 


48.8 


7 


43.5 


13 


46. 8 


AiM-il 


1 


18 


4:1.0 





41.7 


6 


:3G.5 


12 


:39.8 




l."i 


17 


48.0 


2.3 


42.8 


5 


41.5 


11 


44. S 


Mav 


1 


1(J 


45.2 


22 


.39.9 


4 


:38.7 


10 


41.9 




].-. 


15 


,50 :! 


21 


45.0 


3 


43.8 


9 


47.0 


.June 


1 


14 


43. G 


20 


.38.4 


2 


37.1 


8 


40 4 




1.") 


IH 


48.7 


19 


43.5 


1 


42.2 


7 


45.5 


July 


1 


12 


46.1 


18 


40.9 





.39.6 


6 


42 9 




15 


11 


51.2 


17 


46.0 


23 


40.8 


5 


48.0 


August 


1 


10 


44.7 


16 


39.5 


22 


34.3 


4 


41.5 




l.-> 


9 


49.8 


15 


44.6 


21 


39.4 


3 


46. G 


Septembo 


• 1 


8 


43.2 


14 


.•J8.0 


20 


32.8 


2 


40.0 




1.5 


7 


48.3 


13 


43.1 


19 


.37.9 


1 


45.1 


OttobtT 


1 


G 


45.5 


12 


40.3 


18 


:35.1 





42.3 




15 


.5 


50.5 


11 


45.3 


17 


40.1 


23 


43 4 


NoviMubrr 


1 


i 


43.7 


10 


.•38.5 


. 16 


:i3.3 


22 


:36.5 




15 


3 


48.5 


9 


43.3 


15 


38.1 


21 


41.3 


DlTClllbl'l- 


1 


•2 


45.5 


8 


40.3 


14 


35.1 


20 


:iS.3 




15 


1 


M.-i 


7 


45.0 


13 


39.8 


19 


43.0 



AZIMUTH OF POLARIS AT ELOXGATION. 



VEAU. 


25° 


:30' 


;i5 




40 


45° 


50° 


55° 


I'.KK) 


1=21' 


.2 1 24' 


.9 


1" 29' 


.8 


1" 36' 


.0 


1' 44' 


.0 


1 .54' 


.4 


0° 08' .3 


liiOl 


1 20 


.8 1 24 


.G 


1 29 


A 


1 35 


.6 


1 43 


.6 


1 54 


.0 


2 07 .8 


1902 


1 20 


.5 1 24 


.2 


1 29 


.0 


1 35 


.2 


1 43 


.2 


1 53 


.5 


2 97 .2 


1903 


1 20 


.11 1 23 


.9 


1 28 


.7 


1 34 


.8 


1 42 


.7 


1 53 


.0 


2 06 .6 


1904 


1 19 


.8 


1 23 


.5 ' 1 28 


.3 


1 34 


.4 


1 42 


.3 


1 52 


.5 


2 06 .1 


1905 


1 19 


.4 


1 23 


.1.1 27 


.9 


1 34 


.0 


1 41 


.8 


1 52 


.0 


2 05 .6 


1906 


1 18 


.4 


1 22 


.1 


1 26 


.8 


1 32 


.8 


1 40 


.5 


1 50 


.0 


2 05 .0 


1907 


1 18 


.7 


1 22 


.4 


1 27 


.1 


1 33 


.2 


1 40 


.9 


1 51 


.0 


2 04 .4 


1908 


1 19 


.4 1 22 


.1 


1 26 


.8 


1 32 


.8 


1 40 


.5 


1 50 


.6 


2 03 .9 



132 



PLAifE SUKVEYING 




UNITED STATES GEODETIC SURVEY 
Base Map of the United States 

Declinatitjiis west of the lino of zero declination are —. those east are -f~- 




A RAILROAD CURVE IN THE SIERRA NEVADA. CALIFORNIA 

View on th<* line i»f tlie Southern Paoitio Railway, where the ro:ul rouuils Cuih* Horn. In 
nii^uniahious reiriims. theconstru^-li-'U of sueh a curve :»u»t embaxikiuent as here showu pre- 
sui>|»os»-s the most eareful preliminary work l»y survcyinir parties, who, in fact, are the 
pioM.'.'r"^ without who-st- \v.»rk -iii h ron>:trU(^'li-«n \\..!U.i ii.' !nii»-w^ili).'. 



PLANE SURVEYINa 

PART III. 



THE GRADIENTER. 

The vertical circle or arc of the transit or theodolite, under 
ordinary eircuiustances, furnishes the means of measuring the 
vertical ani{le through which the line of coUiniation is turned, or, 
on the other hand, of turning the line of collimation through any 
desired vertical angle. Much of the work of the engineer consists 
in measuring slopes or grades, or in setting a line at a certain 
slope or grade; and the data are given, not in terms of the vertical 
angle directly, hut usually by the amount of rise or fall pc^' 100 
feet. Thus, a rise or fall of 2 feet in 100 feet is designated us a; 
2 per cent grade; a rise or fall of 50 feet to the mile would be' 
designated as a 0.95 per cent grade, etc. The ratio of these two 
quantities, rise (or fall) to reach is evidently the natural tangent 
of the angle of slope; and before the vertical circle can be used for 
setting ofi such elopes, the ratio must be transformed into degrees 
and minutes of arc. 

The tangent-screw of the horizontal axis of the telescope, 
without the aid of the vertical circle, provides the means of quick- 
ly and accurately setting off slopes directly, when the vertical 
angle does not exceed fifteen or twenty degrees. For this pur- 
pose, the ordinary tangent-screw is replaced by a fine screw, with 
very uniform pitch and large graduated head, and also a grad- 
uated scale from which may be read the number of turns or double 
turns made by the screw. The graduated head fits fi-iction-tight 
upon the neck of the screw, so that its index may be made to read 
zero when the line of collimation is horizontal; and it is usually 
divided into fifty parts, so that, after the number of double turns 
is read from the scale, it will give the number of fiftieths of a 
single turn, or hundredths of a double turn. (See Fig. 94.) 

Let the distance of the screw from the axis about which the 
telescope turns, be represented by_ Z and the interval between 



13ft 



PLANE SURVEYma 



the threads by t. If the screw is turned through one revolution, 
tlie lever A D (Fig. 1)4) is moved through the distance DE, and the 
line of collimation through the distance BC, upon the rod PQ. 



Xow 
this i-ati 



, TA,^ DE BC t 

the tangent of the angle DAE = -— j - =: = -- 



To 



the maker of the instrument can give any convenient 

,, and it will be so con- 



200' 



value, but it is customary to make it = 

sidered throughout this discussion. 

If, then, the line of collimation be directed toward the gradu- 
ated rod PC^, the s])Mce over which the line of coHimatiou is 

moved for one revolution of the 




screw IS 



of the distance of 



L'OO 

the r<id from the instrument; 
and the sj)ace ujion the rod over 
\\ hit'li it is moved for two rev- 
2 



hit ions of the screw 



200 



Fis;. !H. 



the screw l? 



ir¥r ^^ '■■''^ above distance.' If 
is turned throuiih less than a sintde revolution, it will be 

35 
indicated upon the graduated head, as, for instance, -^t^ of a single 

7 1 7 

turn, the intercept upon the rod being -rri ^~^t\i\ — m iA ^^ ^^ 

distance from rod to instrument — it being understood, of course, 
that the rod is held perpendicular to the line of collimation in its 
initial position. The index of the graduated head should read 
zero when the line of collimation is horizontal, and the reading of 
the scale of revolutions should be iiero at the same time. 

The gradienter may be used as :i teleuu'ti'r, as a level, or 
sim]>ly as a grade-measurer, as will be explained in what follows. 

Call s the intercept upon the rod for any movement of the 
gradienter-screw, and d the distance from the instrument to the rod. 

If the number of revolutions of the gradienter-screw is known, 
whether s and d are known or not, the tangent of the angle of 
inclination of the line AC is known, and the instrument is a grade- 
measurer or gradienter. 



PLANE SURVEYING 135 

If the space .v and the number of revolutions of the gradienter- 
screw aro known, the distance <1 is known, and the instrument is 
then ii telemeter. 

If the distance d and the number of revolutions of the gradi- 
enter- screw are known, the space *• is known, and the instrument 
then serves the purpose of a level. 

As a gradienter, the instrument may be used either to meas- 
ure the grade of a given line, or to lay out a line to a required 
grade. 

(1.) Let AB (Fig. il5) be the line whose grade is required. 
Set the transit up over the point A, and level carefully. Measure 
the heicrht of the cross-hairs above the ground by holding the rod 
beside the instrument and noting the point upon the rod directly 
opposite the center of the horizontal axis of the telescope. Bring 

the line of colliniatiou CE hori- 
zontal by means of the bubble 
attached to the telescope (the 
instrument is supposed to be in 
adjustment), and set both the 
^ '^- ^°' indexes to zero. Now carry the 

rod to the])oint B, and by means of the gradienter-screw turn the 
telescope in a vertical plane until the line of collimation Strikes the 
point I) as far above B as C was above A. Now count the niimber 
of full turns from the reading of the scale by the 6crew-head, and 
the number of fractions of a turn from the divided head. The 
former will give the rise (or fall) \xifeet per 100, and the latter in 
hundredths of a foot. It must be remembered that if the screw has 
made more than a whole turn past the last number on the scale 
the reading of the head must be increased by fifty. 

Thus, if the reading of the scale is .3 and the reading of the 
head is 35, plus one whole revolution, the rise (or fall) per 100 
feet will be as follows: 

3 douhU turns 3.00 ft. 

1 single turn _ . . _ . 0.50 ft. 
3__5. " ' . - . . . 0.35 ft. 

6 . 

3.85 ft. 
So that the slope of CD, which equals that of AB, is therefore 
3.85 per cent. 




136 



PLANE SURVEYING 



EXAMPLE FOR PRACTICE. 

If the scale reada 2 and the head 31, determine the percent- 
age of elope. 

(2.) It is required to layout in a given direction a line with 
a given percentage of slope from the point A. See Fig. 96. 

Set up the instrument on the given point, as B, and level it 
carefully. Measure the height of the cross-hairs above the ground 
as before, and set the pointers to read zero with the bubble in the 
center of the telescope tube. Now revolve the line of collimation 

in a vertical plane by means of 
the gradienter-screw so as to set 
off the required slope. For in- 
stance, suppose it is required to 
set off a slope of 2.78 per cent. 
The screw should be turned 
five complete revolutions as in- 
dicated upon the scale, plus ||- 
of a revolution as indicated upon the divided head of the screw: 




200 

28 



X 100 ft. 
1 



200 



X iix) n. 



2.50 feet. 



0.28 feet 



= 2.78 feet per 100 feet. 



Now carry the rod to any convenient point, as G, in the direction 
of the required line; hold it in a vertical position; and note the 
heiijht of the line of collimation. Take the difference between 
this and CE (= AB). If this difference, as EG, is positive, it 
gives the Leiglit of the grade line above the ground and indicates 
a Jfll at the point. If the difference is negative, as DE, it gives 
the depth of the grade line lelow the ground and indicates a cut. 

EXAMPLE FOR PRACTICE. 

Let it be required to set off a 3.3.5 per cent grade, and 
describe the operation in detail. 

When the gradienter is used as a telemeter, it may be upon 
level or sloping ground. 

(1.) Upon Level Ground. Set up the transit at one end of 
the line, and level carefully. Bring the bubble of the telescope 
level to the center of its tube, and both gradienter scales to zero. 



PLANE SURVEYING 



137 




Fig. 97. 



Now send the rod to the next station and let it be held vei-tical; 
adjust the target to the line of colliniation and take the reading. 
Now turn the gradienter-screw through two revolutions and take 
the reading again (see Fig. 97). 
The difference of the two read- 
ings gives DE in feet; and since 
the gradienter-screw has been 
turned through two revolutions, 
CE == 100 DE. Thus, if DE 
= 3.25 feet, CE = 325 feet. 

(2.) Upon Sloping Ground. On sloping ground the first 
reading upon the rod cannot be taken with the telescope horizon- 
tal, but the telescope must be revolved in a vertical plane until the 
intersection of the cross-hairs falls at a division upon the rod 
equal to the height of the cross-hairs above the ground at the 
transit station. If now the rod be held perpendicular to the line 
of sio-ht, and the eradienter-screw turned through two revolutions, 

the intercept upon the rod will be — -— of the required distance. 

With the gradienter, as with the stadia, it is more convenient to hold 
the rod vertical and apply the necessary correction to the rod reading. 
Set up the transit over a point at one end of the line and level 
carefully. Measure the height of the cross-hairs above the ground. 
Now loosen the clamp of the tangent-screw attached to the vertical 

arc or circle, and revolve the 
telescope in a vertical plane until 
the intersection of the cross- 
hairs falls upon a point (Eig. 
98) upon the rod held at D, such 
that CD = AB. Read and note 
'^'S- 9S- the vertical angle after clamping 

the gradienter-sci'ew with both scales set to read zero. This angle 
will be 6 (Fig. 98). Now turn the gradienter-screw through 
two revolutions, and note the reading ED upon the rod; the differ- 
ence between this and CD (= AB) will give EC, which call S'; 
let FC, the perpendicular intercept upon the rod, be called S; the 
distance AC, parallel to the slope, H'; and let the horizontal dis- 
tance AG be denoted by II. Then from the figure, 




138 PLANE SLKVEYmG 

H' = 100 S. 
Now, from the right triangle EAG, the angle at E = 90° - 
{0 + <j)); and from the right triangle FAC, the angle at F = 90° 
- e. Therefore, in the triangle CFE, the angle at F = 180° - 
(90° - 0) = 90° + e. 
Therefore, 
S : S' : . sin [90" - {6 + 4>)] : sin (90 + 0); 
or S : S' : : cos (6 -p 0) : cos 0. 

lleiice b = 1? ;, 

COS 6 

cos 6 COS <f> - sin sin 6 
= b' = b' (cos rf> - Bin d) tan 6): 

cos \ -r -r . 

hnt tan — j-rr- , and therefore 8=8' (cos<^ - sin <f> yt^)- 

Tlieref(jre II . the distance along the slcjpe, 

^ 8' ( KM) cos <f> - sin (f>) ; 

and II. the horizontal distance, 

= 11' cos <^ = S' (100 cos- (f) - cos <^ sin <^) 

= b' (1(10 cos' (f) - ^ sin 2 <j)) 

= 100 S' - S' (100 ~sin= <j, ~ h sin 2 (^). 

It may be well to note that the lower reading of the rod need not nec- 
essarily be such as to make CD = AB. but only as a matter of convenience. 

EXAMPLE FOR PRACTICE. 

I'pper rod reading = TIM 
Lower rod reading = 4.67 
\'ertica! angle of lower rod reading — 15' 35'. 
Ile(]uired to find the distance parallel to the slope between B and 
I) and the horizontal distance AG. 

Let it now he required to find the difference of elevation 
between Ji and I) = ('(4. 

Evidently CG = II tan (f> = S' (KXtcos" <f> tan </> - cos (j> .sin 
<f) tan </)). 

= S' (100 sin <f) cos <f> - sin- </>) 
= S' (100 i sin 2(f)- sin- <^i. 
In the last example, determine the difference of level of B 
and I). 

It must not be forgotten of course, that the gradienter used 
in this way cannt)t give results so accurately as the spirit level; 



PLANE SUKVEYIXG 139 



but neveitheless, for rajiid work, the results will be sutticiently 
correct. 

If tbe student possesses a set of stadia reduction tables, the 
values of sin" (f> and -I sin 2 cf) can be taken out at once and much 
labor saved. 

To Lay out a Meridian with the Transit. Jjy means of the 
North Star at I'jijx:)' <ir Lovier C idminaildit. Twice in 24hours 
(more exactly, 23 Lours 56 minutes) the north star "culminates"; 
that is to say, it attains to its maximum distance from the pole, above 
or below it. At the moment of culmination, the star is upon the 
meridian and if, therefore, a line be ranged o"ut upon the ground in 
the same vertical plane, it will define a meridian. 

Set up the transit over a peg, in an open space, giving an 
unobstructed view of a line about 400 or 500 feet loner. Level the 
instrument carefully (it should be in perfect adjustment), and, a few 
minutes before the time of culmination, as given in the table, focus 
the intersection of the cross-hairs upon the star ; clamp the plates, the 
vertical axis, and the horizontal axis of the telescope. Now by 
means of the tangent-screws attached to the vertical axis and to the 
vertical circle, mov^e the telescope in azimuth and altitude, keeping 
the cross-hairs fixed upon the star. After a time it will be found 
that the position of the star no longer changes in altitude; it is 
then upon the meridian. Now clamp the vertical axis, plunge the 
telescope, and carefully center a stake 400 or 500 feet from the 
instrument; the line connecting the two stakes, will define the true 
meridian. 

The whole operation may be repeated several nights in sue 
cession, and the mean of all the results taken. 

By Means of the North Star at Eastern or Western Elon- 
ijatloii. Twice in 24 hours, the north star attains to its maximum 
distance east or west of the pole, called its eastern or w'estern " elon- 
gation." If a line be ranged out upon the ground in the direc- 
tion of the star — at, say, the time of eastern elongation, and again 
at the time of western elongation — and if the ancrle between 
these two lines be bisected by a third line, this last line will evi- 
dently be a true north and south line. 

Otherwise. Having laid out a line upon the gnjund in the 
direction of the north star — say at western elongation — take from 



140 PLANE SURVEYING 



a table the azimuth (or bearing) of the star at such time, and upon 
the horizontal plate of the transit set oS this angle to the east and 
range out a line^which will therefore be a true north and south 
line. If the position of the star is taken at eastern elongation, the 
azimuth must be turned off to the west. 

Set up the transit over a peg a few minutes before the star 
attains its maximum elongation, as given by the table. Level, and 
fix the line of collimation upon the star, following its movement 
as described under the previous method. After a time, it will be 
found that the movement of the star in azimuth ceases; the star 
has then attained its maximum elongation. Now clamp the ver- 
tical axis of the instrument, plunge the telescope, and center a stake 
in the iiroper direction. IS^ow take from the table the proper azi- 
muth, revolve the upper plate through the given angle in the 
proper direction, and range out a line upon the ground for the true 
meridian. 

In order to determine the azimuth of the north star at eastern 
or western elongation, it is necessary to know the latitude of the 
place of observation. 

Dt'jin'(ti(ins. The altitude of a star is the vertical angle at 
the instrument included between the plane of the horizon and the 
line from the instrument to the star, as given by the line of colli- 
mation. 

The latitude of a place is equal to the altitude of the pole. 

If, therefore, we have any method of determining the altitude 
of the pole, the latitude of the ol)server is known at once. 

The altitude of the pole may be determined by observing the 
altitude of the north star, first at its upper culmination and again 
at its lower culmination. The mean of these observations, cor- 
rected fur refraction, will give the altitude of the pole and there- 
fore the latitude of the observer. See tables of refraction of Polaris. 

Set up the transit and level it, and proceed in the same man- 
ner as described under the first method for laying outa trueinerid- 
ian. When the star has reached its maximum distance above or 
below the pole, as indicated by the line of collimation moving in 
a horizontal plane, clamp the horizontal axis of the telescope and 
read the angle upon the vertical circle. The result will be the 
altitude of the star, say at upper culmination. Repeat the operation 



PLANE SUKVEYING 



Ml 



at lower culmination. Now, if A rejjresents the altitude at upper 
culmination, and A; the altitude at lower culmination; t? the refrac- 
tion at upper culmination, and di the refraction at lower culmina- 
tion, then Ap, the altitude of the pole" (= latitude of the place), 
will be given by the following: 

A, :. I- .(A -f A, - d - d,) 

It will be well to repeat these observations and take the mean 
of the results as the probable altitude of the pole. 




Pig. 99. 



THE SOLAR TRANSIT. 

The solar transit is an ordinary engineer's transit fitted with 
a solar attachment. Of the many forms of solars in use, that 
invented by G. I^. Saegmuller, "Washington, D. C, seems to be the 
favorite. In its latest form it is shown in Fig. 99, and consists of 
a telescope and level attached to the telescope of the transit (see 
Fig. 100) in such a manner as to be free to revolve in two direc- 
tions at right angles to each other. When the transit telescope is 
horizontal and the bubble of -the solar in the center of its tube, the 
a axillary telescope with its bubble revolves in horizontal and ver- 
tical planes. 



142 



PLANE SUKVEYING 




PLANE SDKVEYING 143 

If now the line of collimation of the transit be biouirlit into 
the meridian, the telescope pointing to the south, then, if we lay 
off ujion the vertical circle, upward, the co-latitude of the place, 
the polar axle of the solar will be parallel to the axis of the earth. 
If now the two lines of sight are parallel and the solar telescope is 
revolved uj^on its polar axis, it is evident that its line of sight will 
describe a plane parallel to the plane of the e(]uator. If now the 
transit telescope be still maintained parallel to the ecpiator, if we 
turn the solar telescope upon its horizontal axis until the angle 
bet'vi'een the two lines of collimation equals the declination of the sun, 
then when the solar telescope is revolved upon its polar axis, its 
line of collimation will follow the path of the sun for the given 
day, provided thei'e be no change in the sun's declination. If 
therefore the solar telescope is revolved until the image of the sun 
is brought between a pair of horizontal and vertical wires, pro- 
vided in the telescope for that purpose, at that instant the line of 
sight of the transit telescope is in the meridian. 

The horizontal axis of the solar telescope and the polar axis of 
the Bolar are provided with clamjis and tangent-screws by means 
of Mhich careful adjustments may be made. Two pointers are at- 
tached to the solar telescope, so adjusted that when the shadow of 
the one is thrown upon the other, the sun will ajipear in the field 
of view. There are also provided colored glass shades to the eye- 
piece to protect the eye when observing upon the sun. The 
objective and the cross-haii's are focused in the usual M-ay. 

Adjustments of the Solar Transit. It is assumed in what 
follows that the transit is in perfect adjustment, particularly the 
plate levels, the horizontal axis of the telescope, and the zero of 
the vertical circle. 

1. To adjust the Polar Axis. The polar axis should be 
vertical when the line of collimation and the horizontal axis of the 
telescope are horizontal. To make this adjustment, level the tran- 
sit by means of the plate levels. If the telescope is not fitted with 
a level, make the vernier of the vertical circle read zero. Now 
bring the bulible of the solar to the center of its tube and clamp 
the horizontal axis. Loosen the clamp of the polar axis, and turn 
the solar upon its polar axis through 180°. If the bubble remains 
in the center of the tube, the solar axis is in adjustment. If the 



144 PLANE SUKVEYING. 



bubble riina toward one end of the tube, correct one-half of the 
error by revolving the solar telescope upon its horizontal axis and 
the other half by means of the capstan -headed screws at the base 
of the solar. 

If the telescope of the transit is fitted with a level, it will be 
better to test the verticality of the vertical axis by means of it, 
since it is longer and more sensitive than the bubbles upon the 
plate. To do this, revolve the telescope upon its vertical axis 
until it is directly over a pair of diagonally opposite plate arrows, 
and bring the bubble to the center by means of the tangent-screw 
attached to the horizontal axis of the telescope. Now revolve the 
telescope upon its vertical axis through 180 , and note if the bub- 
ble runs to one end; if it does correct one-half the error by the 
jiarallel plate-screw and the other half by the tangent-screw of the 
horizontal axis, and repieat this test and correction until the bubble 
remains in the center in all positions. 

2. To Adjust the Cross-Hairs of the Solar. The line of 
coUiniatioD of the solar telescope should be parallel to the line of 
coUiuiation of the tran.sit telescope. The first adjustment having 
been made, first bring the telescope into the same vertical plane by 
centering a stake by the transit telescope and clampiing the verti- 
cal axis. Now turn the telescope of the solar upon the polar axis 
imtil the intersection of the cross-hairs covers the same point upon 
the stake, and clamp the polar axis. Now level both telescopes 
by bringing the bubbles to the center, and measure the distance 
between the axes of the two telescopes; draw at this distance two 
black parallel lines upon a piece of white paper. Tack up the 
paj)er against a wall, post, or other convenient oV>iect, adjusting it 
in position so that one black line is covered by the horizontal cross- 
hair of the transit telescope; notice if the other black line is cov- 
ered by the horizontal cross-hair of the solar; if so, the adjustment 
is completed; otherwise, move the diaphragm carrying the cross- 
hairs of the solar, until the second black line is covered. Adjust- 
ing the cross-hair diaphragm may displace the solar telescope ver- 
tically, BO that the bubble should again be brought to the center of 
tho tube, and the adjustment tested and repeated until the two 
lines of collimation are j)arallel, when the two bubbles are simul- 
taneously in the center of the tubes. 



PLANE SURVEYING 145 

The Use of the Solar Transit. An observation with the 
solar transit involves four quantities as follows: 

1. The time of day, that is to say, the hour-anglo of the sun. 

2. The clechnation of the sun. 

3. The latitude of the place of observation. 
i. The direction of the meridian. 

Any three of these quantities being known, the fourth may be 
determined by direct observation. The principal ii^e of the solar 
transit is to determine a true meridian when the other three quan- 
titles are known. 

To Lay Out a True Meridian. Set up the transit over a stake; 
level the instninient carefully; and bring the linea of collimatiou 
of the telescopes, into the same vertical plane by the method pre- 
viously described. Take the declination of the sun a3 given in the 
Kavticol Ahnanao for the given day, and correct it for refraction 
and hourly change. Eevolve the trfinsit tel('f«:(>j>e upon its hori- 
zontal axis so that the vertical circle will record this coi-rected dec- 
lination, turning it down if the declination is north, and elevating 
it if the declination is south. Kow, without disturbing the posi- 
tion of the transit telescope, bring the solar telescope to a horizon- 
tal position by means of the attached level. It is evident that the 
angles between the lines of colliniation will equal the corrected 
declination of the sun, and the inclination of the solar telescope 
to its polar axis will be equal to'the polar distance of the sun. 

Next, without disturbing the relative positions of the two tele- 
scopes, set the vernier of the transit telescope to the co-latitude of 
the place, and clamp the horizontal axis. It is evident that the 
transit telescope is parallel to the equator, and that the solar tele- 
scope is in a position to describe the path of the sun when the line 
of coUimation of the transit is iyi the true vneridtan; and unless 
the line of collimation is in the true meridian, the sun cannot be 
brought between the cross-hairs of the solar telescope. Therefore 
unclamp the vertical axis of the transit and the polar axis of the 
solar, and, maintaining the relative positions of the telescopes 
revolve the transit upon its vertical axis, and the solar upon its 
polar axis, until the sun is brought between the cross-hairs of the 
solar telescope. Now clamp the vertical axis of the transit and 
range out a line upon the eround for the true meridian. 



146 PLANE SUEVEYING 

Tlie solar apparatus should not be nsed between 11 a. m. and 
1 r. M. if tlie be!?t results are desired. From 7 to 10 a, m. and 
from 2 to 5 p. m. in the summer will give the best results. The 
greater the hour-angle of the sun, the better the observation will 
be so far as instrumental errors are concerned. However, if the 
sun is too clo.se to the horizon, the uncertainties in regard to refrac- 
tion will cause unknoM-n errors of considerable magnitude. 

OJiiii'rvtitiinv for Time. If the two telescopes — being in 
position, one in the meridian and the other pointing to the sun — 
are now revohed upon their hurizdutnl axes (the vertical remaining 
undisturbed) until each is level, the angle upon the horizontal 
j)late between their directions, as found by sighting on a distant 
object, will give the time from apj)arent noon, reliable to within a 
few seconds. 

To Determine the Latitude Level the transit carefully, and 
point the telescope toward the south, setting olf the declination of 
the sun upon the vertical circle, elevating the object end if the dec- 
lination is south, and depressing it if the declination is north. 
Being the telescope of the solar into the same vertical plane with 
the transit telescope by the method previously described, level it 
carefully, and clamp it. The angle between the lines of collimation 
will then e(]ual the declination of the sun. With the solar tele- 
scope, observe the sun a few minutes before its culmination, by 
moving the transit telescope in altitude and azimidh until the 
imafe of the sun is brought between the cross-hairs of the solar, 
keeping it there by ineansof the tangent-screws until the sun ceases 
to rise. Then take the reading of the vertical circle, correct for 
refraction due to altitude by the table below, subtract the result 
from 90", and the remainder is the latitude sought. 



PLANE SUKVEYING 



147 



Mean Refraction at Various Altitudes.* 

liaroraoter, .'iO inches. Fahrcahoit Thormomrtir. .'in , 



Altituil- 


Eefr 


actidii. 


Allitudo. 

'20 


Refraction. 




10 


-. 


19" 


•)' 


:59" 




u 


i 


51 


25 




04 




12 


i 


27 


30 




41 




13 


i 


07 


35 




•23 




14 


3 


49 


40 




09 




15 


3 


34 


45 




58 




■ 16 


3 


•20 


50 




49 




17 


3 


08 


(iO 




34 




18 


-) 


57 


7(1 




21 




I'J 


•> 


4H 


M> 




10 





Preparation of the Declination 5ettings for a Day's Work. 

The solar epliemeris gives the declination of the sun for the given 
day, for Greenwich mean noon. Since all points in America are 
west of Greenwitji. by -i, 5, (>, 7, or <S hours, the declination found 
in the ephenieris is the declination at the given ])lace at 8, 7, G, 5, 
or 4 o'clock a. m. of the same date, according as the place lies in 
" Eastern ", " Central ", " Western ", " Mountain ", or '• Pacific " 
time belts respectively. 

The columns headed "Refraction Corrections" (see table) 
give the correction to be made to the declination, for refraction 
for any point whose latitude is 40'. If the latitude is more or less 
than 40°, these corrections are to be multiplied by the correspond- 
ing coefficient given in the table of " Latitude CoefKcients" (page 
148). Thus the refraction corrections in hxtitude 30 are G5 one- 
hnndredths, and those of 50° 142 one-hundredths of the correspond- 
ing ones in latitude 40'. There is a slight error in the use of 
these latitude coefficients, but the maximum error will not amount 
to over 15 seconds, except when the sun is very near the horizon, 
and then any refraction becomes very uncertain. All i-efrac- 
tion tables are made out for the mean (or average) refraction 
whereas the actual refraction at any particular time and jilace may 
be not more than one-half or as much as twice the mean refraction, 
with small altitudes. The errors made in the use of these latitude 
coefficients are therefore very small compared with the errors re- 

* This table, as well as those following, is taken from the catalogue of 
George N. Saegmuller, Washington, D.C. 



148 



PLANE SUKVEYING 



snlting from the use of the mean, rather than unknoMn actual, 
refraction •which affects any given observation. 



Latitude Coefficients. 



LAT. 

• 


COEFF. 


I»A.T. 


COEFF. 


LAT. 


COEFF. 


LAT. 


C»EPF. 


15° 


.30 


27^ 


.56 


39° 


.96 


1 51° 


1.47 


IC 


.32 


28 


.59 


40 


1.00 


52 


1.53 


17 


.34 


29 


.62 


41 


1.04 


53 


1.58 


18 


.36 


30 


.65 


42 


1.08 


54 


1.64 


19 


.38 


31 


.68 


43 


1.12 


55 


1.70 


20 


.40 


32 


.71 


44 


1.16 


56 


1.76 


21 


.42 


33 


.75 


45 


1.20 


57 


1.82 


22 


.44 


34 


.78 


46 


1.24 


58 


1.88 


23 


.46 ' 


35 


.82 


47 


1.29 . 


59 


1.94 


24 


. .48 


36 


.85 


48 


i.as 


60 


2.00 


25 


.50 


37 


.89 


49 


1.38 






26 


.53 


^8 


.92 


50 


1.42 







If the date of observation be between June 20 and September 
20, the declination is positive and the hourly change negative; 
while if it be between December 20 and March 20, the declination 
is negative and the hourly change positive. The refraction cor- 
rection is always positive; that is, it always increases numerically 
the north declination, and diminishes numerically the south dec- 
lination. The hourly refraction corrections given in the ephem- 
erJB are exact each for the middle day of the five-day period, cor- 
responding to that of hourly corrections. For the extreme days 
of any such period, an interpolation can bo made between the 
adjacent hourly corrections, if desired. 

By using standard time instead of local time, a slight error 
is made, but the maximum value of this error is found at those 
points when the standard time differs from the local time by one- 
half hour, and in the spring and fall when the declination is chang- 
ing rapidly. The greatest error then, is less than 30 seconds, and 
this is smaller than can be set off on the vertical circle or declina- 
tion arc. Even this error can be avoided by using the true dif- 
ference of time from Greenwich in place of standard meridian 
time. 

EXAMPLES FOR PRACTICE. 

(1) Let it be required to prepare a 'able of declination for 
June 10, 1904, for a point whose latitude is 40° 20' , and which 
lies in the " Central Time " belt. 



PLANE SUKVEYIXU 



1-19 



Since the time is () hours earlier than that at Greenwich, the 
declination given in the ephemeris is the declination at the given 
place at G a. m. of the same date. This is found to be 23^ 0' IS". 
To this must be added the hourly change which is also plus and 
equal to 11. HT". The latitude coefficient is 1.013. The follo\vin<r 
table nuiy now be made out. 





PKriJNATION. 


KBP.COH 


>i:i TIN.;. 


HOXJB. 


7 

8 

9 

10 

11 


- 23^0' 30"'+ r 10" 
1-23 0'41"|+ 44" 
4-2.3'0'5:ri+ 29" 
+ 2.3^' 5"+ 22" 

-!-23 1'17"+ IS" 


2.3' 1' 40" 
23^ 1' 25": 
2.3 ' l' 22", 
23=1' 27" 
23'1'.35" 


1 

2 
3 

4 
5 



DECIJKATION. I REF. COR. 

I 



4- 2.3' 1' 29"!-f- 18" 
+ 23' 1' 41"'+ 22" 
+ 23'1'5:3"+ 29" 
+ 23^ 2' 5"1+ 44'' 
+ 2.3'2'17":+l'l(V 



SETTIKU. 


23' 


1' 


47' 


23 


2' 


3' 


23' 


2' 


22 


23 


2' 


49 


23 


3' 


27 



PROBLEMS INVOLVING USE OF TRANSII . 

Perpendiculars and Parallels. To erect a pc',2>,-ii<]iriihir to 
a liiiii at a, givi'iv 2>"'i'i "f ^J"' ^'>'<^- Set up the transit over the 
given point, and with the verniers set to 0', direct the line of 
sight along the given line. Clamp the lower motion, unclamp the 
upper motion, and turn off an angle of 00^ in the proper direction 
for the required line. 

To eriict a pi'/rj:>endk-Hlar to an inaccessible line at a ijiven 
Ijohitoftheli.ne. Let AB, Fig. 101, be the given inaccessible 
line, and A the point of the line at which it is proposed to erect 
the perpendicular AD. Select 
some point II from which can be 
distinctly seen the points A and 
B of the inaccessible line. Set up 
the transit at the point H, and 
measure theantrle AIIB. Also 
from the point II run out and 
measure a lineof any convenient 

leno-th, and in such a direction that the points A and B can be 
seen from its extremity, as E. Now measure the angles AHE 
and BIIE. Now set up the transit at E, and measure the angles 
BEH, BEA, and AEH. In the triangle AHE, we know 
from measurement the length of the side HE, as also the angles 
AHE and AEH, from which may be calculated the length of 
the side AH, which is also one side of the triangle AIIB. From 
the triangle BEH, we have the length HE, known by measure 




150 



PLANE SURVEYING 



Refraction Correction. 

Liitilud.', 40 . 



January. 


February. 




March. 


1 


ih. 1 r,s 


1 






1 


Ih 


1 Oi 


2 


2 2 16 


'2 






.) 




1 10 


3 3 04 








~ 


3 


1 27 


3 


4 fi 23 








i 


4 


2 06 






3 


111 


1 26 


i 


5 


4 39 


fi 


2 2 U 


4 


2 


1 37 




1 


59 


fi 


6 

7 


3 


2 04 


6 


2 


1 06 


7 
K 


4 i; 01 


4 


3 21 


7 

8 


3 
4 


1 21 
1 .56 


9 


1 1 51 


f 


1 


1 21 


9 


5 


4 01 


10 
11 
12 

la 


2 2 07 

3 2 51 

4 5 40 


10 
11 
12 


I 


1 31 
1 .56 
3 04 


10 
11 
12 
13 


1 

2 
3 
4 


55 

1 02 
1 15 
1 47 


u 


1 1 40 


13 

11 


1 


1 16 

1 25 


14 


1 

2 
3 
4 


3 34 
.52 

5S 

1 10 
1 39 


Hi 

n 

IS 


2 2 01 

3 2 40 

4 500 


llj 
17 


3 
4 


1 48 

2 47 
8:,9 




19 
20 


1 1 42 

2 1 56 


18 
19 
20 


1 
1 
3 


1 12 

1 20 
1 40 


19 
20 


5 
1 


3 08 
048 
54 




3 2 31 


21 


4 


2 31 
6 49 


r?. 


3 


1 tt5 


n 


4 4 35 


..- 


•* 


23 


4 


1 32 


•>i 


1 1 37 


23 


1 


1 07 


24 


•' 


2 51 


2o 
26 
27 

2K 


2 1 58 

3 2 22 

4 4 07 


24 

•>5 

2(i 
27 


.3 
4 


1 33 

2 18 
5 28 


26 
28 


1 

i? 

4 


45 
(1 .50 

1 01 

1 25 


"X) 


1 1 "2 


28 






29 


'■> 


2 34 




2 1 41 








30 


1 


42 


M 


3 2 13 








31 


2h 


47 


31 


4h. 3 41 















April. 



.0 57 

1 19 

2 18 
.39 
44 

54 

1 U 

2 08 

36 
41 

51 

1 10 
1 58 

34 
38 

48 

1 06 
1 49 



1ft 


1 


32 


20 


2 


36 


21 


3 


45 


22 


4 


1 02 


23 


5 


1 42 



30 
34 
42 

58 

1 36 

28 
32 



May. 



Ih. 28 

2 .32 

3 .39 

4 55 

5 1 30 

1 26 

2 30 

3 37 

4 53 

5 1 26 

1 25 

2 29 

3 :.6 

4 51 

5 1 22 

1 23 

2 27 

3 34 

4 49 

5 1 18 

1 22 

2 26 

3 33 

4 47 

5 1 15 

1 21 

2 25 
■■', 32 

4 40 

5 1 13 

1 20 

2 24 
4 31 

4t 



jh. 1 U 



Juuo. 

Sh. 1 u 



1 


019 


2 


23 


3 


om 


4 


43 


o 


1 10 


1 


18 


2 


22 


3 


29 


4 


43 


■1 


1 09 


1 


1S 


2 


22 


;; 


"29 


4 


1)42 


■I 


1 OS 


1 


1H 


2 


22 


',', 


28 


4 


4^ 


5 


108 


1 


18 


J 


22 




29 


4 


42 


:j 


1 08 


1 


18 


2 


22 


3 


29 





July. 




Vugnst. 


September. 


October. 


November. 


December. 


1 


5h 


1 09 


1 






1 


Ih. 39 


1 


Ih 


.59 


1 


2h 


3 21 


1 


Ih 


1 54 














2 


2 44 


2 




1 «! 


2 


3 


13 .57 


., 


9 


2 11 


3 
4 


1 

.3 


19 
2:1 
030 


3 
4 


Ih 

2 

3 


26 
30 
37 


3 
4 


3 54 

4 1 14 

5 2 08 


3 
I 




1 21 

1 .".6 
4 04 


1 


4 
1 


1 .32 


3 
4 


3 
4 
5 


2.59 
6 01 


fi 


4 


43 


5 


4 


53 


6 


1 42 


6 




1 03 


6 


9 


1 44 


5 


1 


1 58 


i 


rj 


1 10 


6 


5 


1 26 


7 


2 47 


7 




1 10 


7 


3 


2 13 


6 




2 16 


8 
9 
10 


1 
3 


20 
24 
31 


8 
9 


1 
2 
3 


028 
.32 
39 


8 

iS 


3 57 

4 1 19 

5 2 18 


8 
9 
10 




1 27 

2 06 
4 39 


8 
9 
10 


4 

5 

1 


3 41 
1 .37 


8 
9 


3 
4 


3 04 
6 23 


11 


4 


44 


10 


4 


55 


11 


1 45 


11 




1 07 


11 


9 


1 .50 


1(1 


1 


2 00 


12 


5 


1 11 


11 


5 


1 30 


12 


2 .50 


12 




1 15 


12 


3 


■1 .>•> 


11 




2 19 


13 
14 
15 


1 
3 


21 
25 
.32 


12 
13 
14 


1 

2 
3 


.^0 
34 
42 


13 
11 
15 


3 1 01 

4 I 25 

5 2 34 


13 
14 
15 




1 33 

2 18 
5 39 


13 
11 

15 


4 
5 

1 


4 07 
1 42 


12 

13 
14 


3 
4 


3 09 
6 38 


16 


4 


46 


1.5 


4 


.58 


16 


1 48 


16 




1 12 


16 


2 


1 .56 


15 


1 


2 01 


17 


5 


1 13 


16 


.'j 


1 36 


17 


2 .54 


17 




1 20 


17 


;j 


2 31 


1 i 




2 20 


18 
19 
IH) 


1 

2 
3 


22 
26 
33 


17 

18 
19 


1 

2 
3 


032 
0S6 
45 


18 
19 
20 


3 I 05 

4 1 .32 

5 2 51 


18 
19 
20 




1 40 

2 31 
6 29 


IS 

19 
20 


4 
5 
1 


4 35 
1 46 


li 
IS 
19 


4 


3 11 
6 47 


21 


4 


47 


20 


4 


1 02 


21 


1 .52 


21 




1 16 


21 


9 


2 01 


20 


1 


2 01 


22 




1 15 


Li 


5 


1 42 


22 


2 U 58 


99 




1 25 


22 


3 


2 40 


21 




2 20 


23 
24 

25 


1 

.3 


23 
27 
34 


24 


1 
2 
3 


0.34 
0.38 
48 


23 
24 
25 


3 1 10 

4 1 39 

5 3 08 


23 
24 

25 




1 48 

2 47 
8 39 


23 
24 


4 
5 
1 


4 .59 
1 .50 


9» 

2.3 
24 


3 
4 

5 


3 11 

6 49 


26 


4 


49 


**'> 


4 


1 06 


26 


1 or.5 


26 




1 21 


26 





2 06 


25 


1 


2 00 


27 


5 


1 18 


26 


5 


1 49 




2 1 02 


27 


2 


1 31 


27 


3 


2 4!l 


2(> 




2 19 


28 


1 


25 

SO 
.36 


27 
28 
29 


1 
2 
3 


0.";6 
41 
51 


2K 


3 1 15 


28 


3 


1 .51) 


:'.s 


4 


5 33 


27 


3 


3 09 


29 


4 1 47 


29 


4 


3 04 


29 


5h 




28 


4 


6 4:1 


29 


3 


30 


5h. 3 .34 


:jo 


ih 


11 01 
126 

1 .37 

2 04 


30 






29 


5h 




.-iO 
31 


4 
5h 


51 

1 22 


m 


4 

5h 


1 10 

. 1 58 






31 








30 
31 







PLANE SURVEYING 151 



meiit, as well us the aniiles BllE and BEII, from which we 
can calculate the length of the pide BTl, wliicli is also one side of 
the trianiTle AllB. Therefore in the triangle AIIB, we have 
the leui'ths of the two sides All and BII hy calculation; and the 
ancrle AIIB by nieasureiueiit. AVe can therefore calculate 
the angle IIAB, which equals the angle AIID. Set up tlie transit 
at II, siidit to xV, and turn off the angle AllD (-^ IIx\B), 
measurino- off II I) of a length equal to All cos AIID. Then 
AD will be the jierpendicular required, and its length will equal 
All sin AIID. 

The calculation is as follows: In the triangle AIIE, the angle 
HAE -^r: ISO'- (AIIE -I- AEII), and therefore All : HE : : sin 

AEIl : sin IIAE; or. All = HE ^!"-;\^. t- 

Bin liAK 

In the triangle IlEB, IIBE = ISO - dUlK liKllj, and 

therefore IIB : HE : : sin llEI! : sin lliiE; 

TTT> TIT? ^^" IIEB 

or IIB = HE -,_^^. 
sm 11 BE 

In the triangle AIIB, the sum of the angles If.VB and IIBA 

— 180' - AIIB. Let X represent the difference of the angles 11 AB 

and HBA. Then, from trigonometry, 

AH + IIB : All - IIB :: tan I (II AI! ili'.A, : tan I (HAB- 

IIBA); 

or, AH + HB : AH - HB :: tan i (INO' ^ AIIB) : tan -I a-; 

or, AH + HB : AH- HB :: cot ^^^r tan l .,■. 

From this last proportion we find r, thedifEerenceof the two angles 
HAB and IIBA. We then have the simultaneous equations: 

IIAB ! HBA = c(say) 

HAB - HBA = ,1 (say) 

Therefore HAB = " \ '^ ; and IIBA = '-',—. 

KXAMPLE FOR PRACTICE 

Given HE (Fig. 101) = 125 feet;xVIIE= 122'; AHB :^ 94"; 

BHE=28°; BEII = 121°; BEA = 80 ; AEII = 41'. It is required 

to find the angle AIID, the length of HD, and the length of AD 

Aus. AHD-== 50" 54'; HD = 17(3.92 feet; AD = 217.92 feet 



152 



PLANE SURVEYING 



To let full a perpendicular ton line from a cjiven point. 
Let AB, Fig, 102, be the given line, and C the point. Set up the 
transit at some point A of the given line, and measure the angle 
BAG. Take the instrument to C, sight to A and tarn off an angle 
AOB = 90' - BAG. The instrument will then sight in the direc- 
tion of the required perpendicular CB. 

To let fall a perpendicular to a line from, an i?iacoessiMe 
point. LetBG, Fig. 103, be the given line and A the inaccessible 
point froyi which it is desired to let fall the perpendicular upon 
Be. Set nji tlie instrument, as at B; and, after measuring the 




B- 



D 

Fig. 1()2. Kig. 103. 

length of BG, measure the angle ABG. Take the instrument to 
ind measnre the angle ACB. Then in the triangle ABC, 
AB : BC : : sin ACB : sin (ACB + ABC); 

AB = BC 



(' 



sin ACB 



and. 



sin (ACB + ABC)' 
BD = AB cos ABC; 

BD = BC *^° ^^^ 



tan ACB + tan ABC" 



EXAHPLE FOR PRACTICE. 

Given BC (Fig. 103) = 250 feet; ABC = 03^15'; ACB = 
o5 40'. Calculate the length of lU), and the length of AD. 

) BD = 100.2 feet. 
^"'- ) AD = 210.7 feet. 
To let fall a perpendicular to an inaccessible line from a 
given point outside of the line. Let AB, Fig. 104, be the inacces- 
sible line, and C the point from which it is desired to let fall the 
perpendicular to AB. Through C run out and measure a line 
of any convenient length, as CD, and measure the angles ACB 



PLANE SUEVEYIXG 



153 




turned ott' equal to CAI!, the 



DCB, and DCA. Set up the instrument at J), and measure the 
anifles ADC and BDC, In the triangle BDC, we have given two 
angles and the inehided side, fn)m whicli can be calculated the 
length of the Bide CB, In the triiingle ADC', wo have given two 
anirles and the included side, from which can ba calculated the 
length of the side AC. Then, in the triangle ACB, we have 
the lengths of the sides AC and CB, and the included angle 
ACB, from which can be calculated the angle CAB. If, then, the 
instrument be set up at C, and an angle ACIC 1>e turned off equal 
to 90' - BAC, the line of sight 
will point in the direction of the 

i A E B 

required perpendicular, and the 
length of the perj)endicular will 
be giviMi by AC cos ACE. 

This same method will serve 
to trace a line th rough a give n 
■point jjaTaUcl to an iiiacce-tsi- 
hle line. For if, with the instru- 
ment at C, an angle ACxi' \n 
line A' B' will be parallel to AB. 

Obstacles to Alignment. Jii/ I'erjjendiculars: When a tree, 
house, or other obstacle obstructing the line of sight (see Fig. 105) 
is encountered, set up the transit at the point B, turn oif a right 
ancle, and measure the length of the line BC. Erect a second 
perjiendicular CD at C, and measure its length. At D erect a 
third perpendicular I)E, making DE = BC. Then the fourth 
perpendicular EF will be in the direction of the required line. 
The distance froju B to E will 'be given by CD. If perpendic- 
ulars cannot be conveniently set off, let BC and DE make any 
equal angle with the line AB, so that CD will be parallel to it. 

Bij an Equilateral Triamjle. At B turn off from the direc- 
tion of AB produced, an angle of 60' in the direction of BO (see 
Fig. 100), and make BC any convenient length sufficient to clear 
the obstacle. Set up the instrument at C and turn off an angle of 
60° from BC to CD and make CD of a length ecjual to BC 
Finally at D turn off a third angle of 60' from CD to DB, and 
the line DE will be in the direction of AB produced. The dis- 
tance BD will equal BC or CD. 



154 



PLANE SURVEYING 



Jlij Trlanyulatiini. T-t-t AB, Fig. 107, be the line to be 
jirolouged beyund tlie obstacle. Choose some point as (' from 
which can be seen the lino AB as well as some point D i)e^ ond 
the obstacle. "With the transit at A, measure the length of AB 
;ind measure the angle BA(". Set up the transit at (', and meas- 




I'i^'. 105. 

ure the aiiirles BCA uiid At'i). Then, in the trianifle ACB, 
we have one side and two anglea known, from which can be cal- 
culated the lengths of AC and BC. In the triangle ACD, we 
know the length A(5 and the angles BAC and ACD, from 
which can be calculated the length CE, the angle BEC, and the 
distance AE. Therefore from C measure the distance CE, set up 
the transit at E, and turn off the angle CEF equal to 180° minus 
the angle BKC, for the direction of the required hue. The 
length of BE will evidently equal AE - AB. 

By a liaiidotn J. 'me. When a wood, hill, or other obstacle 
prevents one end of a line (as B, Fig. 108) being seen from the 
other end A, run out and measure a random line, as AC, as 



y\^. 107. 



---e> 



x^<^'^ 



.Q'^^- 



Fig. lOS. 



nearlv in tiie I'equired direction a.s may be guessed, until a jioint 
C is reached from which V> can be seen. Now, if cunvenieiit, 
measure the perpendicular offset from AC to tlu' point V>, from 



which can be calculated tlie anyle CAB. Ta 



CAB = - 



BC 
AC 



If a right angle cannot be turned off at (\ turn off any convenient 
angle and measure the distance CI!; tlicii, in the triangle ACB, 
there are given two sides and the included angle, from which can 
be calculated the angle C.M!. Kow taking the transit back to 
A, the angle CAB can be turned off in tlie proper direction from 



PLANE SURVEYING 



155 



AC, and the correct line AB can lic run out and mcasuri'd in 
the proper direction. 

By Latitudes and I)ij)firt iircn. "When a single line such as 
AC cannot be run so as to come opposite the given point B (Ficr. 
100), a series of zigzag lines (as AC, CD, I)E, EF, and FB) can 
he run in any convenient directit)n, so as at las*^ to arrive at the 
desired point B. Any one of 
these lines I as. for instance, AC) 
may be taken as a meridian to 
which all of the others may be 
referred, and their bearings there- 
from deduced. Calculate the 
total latitudes and departures of 
these lines, as AX and BX; then 
the bearing of the required line BA with respect to AC will be 

BX 

given by Tan. BAC = Xv"" 

By I'riatujidatiiju. When obstacles prevent the use of 
either of the preceding methods, if a point C can be found from 
which A and B are accessible (see Fig. 110), measure the dis- 
cances CA and CB, and the angle ACB, from which can be calcu- 
lated the length of the side AC and the angle CAB. Now 

measure the angle ACD to some 




Fi<r. 100. 



-<h-cSi-^^0^ 




point D beyond the obstacle; 
then, in the triangle ACD, we 
have two angles and the included 
side, from which may be calcu- 
lated the length of the side CD. 
Measure the distance CD in the 
proper direction, set up the tran- 
sit at D, and turn olf an angle CDB e(pial to the supplement of 
ADC, for the direction of the required line. 

The distance from A to D may also be calculated from the 
triangle ACD, the stake at D given its proper number, and the 
line continued. If the distances CA and CB cannot be meas- 
ured, it will be necessary to measure a base-line through C, from 
the extremities of which the autrles to A and 1] can be measured 

o 

and the reauired distances calculated as before. 



156 



PLANE SURVEYING 



The following jirobleni, as illustrated iu Fig. 111. is of fre- 
(juent occurrence in line surveys. The line AB of the survey 
having been brought up to one side of a stream, it is desired to 
continue the line of the survey across the stream to the point C, 
the latter point being visible from B and accessible. It is required 
to find the lenorth of the line BC, that the stake at C may be given 
its ])roper number, and the survey continued from that point. 
With the transit at B. turn off the recjuired angle to locate the 
point (', and drive a stake at that point. If possible, deflect from 
BC a riglit angle to some point E, and measure the length of BE. 
Take the transit to E, and nieasui-e the angle BEG. The dis- 
tance BC is therefore: 

BC = BE tan F>EC. 

If it is not possible to turn off it right angle at B, then through 
l> run a line (as BE' ) in any convenient direction, and measure 
its lenijth; measure also the angles E'BC and BE'C. In the 
triangle CBE'. there are then given two angles and the included 

side, from which the side BC can 
be calculated. Should it be nec- 
essary to take soundings at cer- 
tain intervals (as, say, 50 or 100 
feet across the stream), then in 
the triangle BE X there are given 
the distance BX, the distance 
E'X, and the angle XBE'. from 
which can be calculated the angle BEX. With the transit at E', 
turn off from BE' the angle BE'X. Now. starting a boat from 
the shore, direct it in line from B to C until it comes upon the 
line of sight of the transit from E' to X. At that point take 
soundings, and similarly for the point X', etc. If the point C is 
not visible from B,find some point, as E (see Fig. 112), from which 
H and C are visible, and nu^asure the angle BEG and the distance 
EB. Find a second poin.t, as ¥, from which E and are visible, 
and measure the angles CEF and EEC and the distance EF. Then, 
in the triangle ECF, there are given two angles and the included 
side, from which can be calculated the distance EG. In the tri- 
angle I!CE. tluMi, there are given two sides and the included 




Fig. 111. 



PLANE SURVEY ING 



157 



angle, and from these the third side BC and the augle EBC can 
be found. The stake C can now be numbered, and the bearing of 
BC deduced. 




EXAMPLES FOR PRACTICE. 

1.' In Fig. Ill, given BE' = 210 feet; angle CBE' = 110^ 

15'; angle BE'C ^ 3i 20'; stake B numbered 8 -|- 54. It is 

required to tind the number of the stake C. 
2. (a) In Fig. 112, given 

EF = 250 feet; BE = 128 feet; 

angle EFC = 40 40'; angle CEF 

= 108' 30'; angle BEC = 39° 10'. 

If the stake at B is numbered 12 

+ 20, it is required to lind the 

number of the stake at C. 

(h) If the bearing of the line 

AB is S 75'E, and the deflection 

angle of BE from AB is 104- to the right, find the liearing of BC. 
To Supply Omissions. Any two omissions in a closed sur- 
vey — whether of the direction or of the length, or of both, of one 

or more lines of the survey — can always be supplied by the 

application of the principle of lati- 
tude and departures, although this 
method should be resorted to only 
in cases of absolute necessity, 
since any omission renders the 
checking of the field work im- 
[lossible. In the following para- 
graphs, the methods outlined will 
apply equally whether the survey 
has been made with the transit 
or with the compass. 

C.\SE 1. W/te7i the length 
and hearing of any one side a/re 
wanting. In Fig. 118, let the 
dotted line FG represent the 
course whose length and bearing 

are wanting. Calculate the latitudes and departures of the remain- 




ir,8 



PLANE SURVEYING 



different; of the loniritndt's wil 



Taiim'iit oi I'e.i 



ini^ courses; and since in a closed survey the algebraic sum of the 

latitudes and deiiartures should eijual zero, therefore the difference 

of the latitudes will he the latitude of the niissincr line, and the 

he the recjuired loncritude. The 

latitude and longitude of the line, 

form the sides of a right triangle, 

from which we have: 

Longitude 

Latitude 

The reipiii'ed length will he given 

Latitude 

hy L = -^ ^ -. — . 

Los LJeanng 

Cask 2. W/i,i>, f/,r hiiijtl, of 
1)116 siile anil fill' Jniinn<i <if mi- 
otlu't'iire ir'iiitniii. 

{(/) Whkn the deficient 

SIDES AD.KlIN EACH OTHER. lu Fig. 

114:, let the hearing of DE, and 




ihe length 
Draw DF. 



!•>. 114. 

of I''K, lie lacking. 
From the preceding 



|)ro]iosition we can calculate the 
hearing and lentjth of DF, as 
though DEand EF did not exist. 
Then, in the triangle DEF. we 
have tjiven the lengths DF and 
DE and the angle DEF, from 
which can he calculated the angle 
FDE and the length EF. 

if>) ^\' 1 1 ic N T\{ I ; D K E n ■ I !•: n r 

SIDES AKE SI'II'.V l; Al |:D EUilM l:\lll 

oTHEi;. in Fig. IF") let A1}(-1)E 
1"( i A re|ii'eseMt a seven-sided 
tield. in which the length of CD, 
and the liearing of Fti, are want- 
ing. Draw Dir, li'A', A'(V, of 
the same lengths, and jiarallel 
respectiveiv to CI!, DA. and A(; 




Pig. 115. 



Connect (i'willi (iEand F. 



Then. Ml tile figure DB' A'(-i'I'j, there are given the lengtiis aii< 



PLANE SURVEYING 



159 



beariniTs of all of the courses but G'E. The length and bearing ol 
the last course can be calculated by the principles of Case 1. Then, 
in the triangle EK(i . there are given the lengths and bearings of 
EF and E(t'. from which can be calculated the length and bearing 
of FCt'. Therefore, in the triangle (tF(i', since GG' is equal in 
length and parallel to CD, there are given the Icniitha of GF and 
FG', and the bc<ir'nHjs of V\(j' and FG', from which can be cal- 
culated the length of GG' and the bearing of CrF. 

Cask 3. Wlun. the letKjiJis of tiro ^■it/ca arc irdiithnj. 

{^ir') When tiik djcficiknt sidks ao.ioin kach other. In the 
seven-sided Fig. 116, let the lengths of DE and EF be wanting. 
Calculate the length and bearing of DF by the principles of Case 1. 
Then, in the triangle EDF, there 
are given the angles at D and F, 
and the length of DF, from which 

- o 

caii be calculated the lengths of 
DEandEF. 

(/') AViIKN THE DlCFIClliNT 
SIDES AKl/ SEl'AKATED FROM EACH 

OTHER. In Fig. 115, let the a~ 
lengths of CD and GF be want- 
ing. As before, having calculated 
the length and bearing of FG'. 
in the triangle FG(t', the angle at ^ 
G can be calculated from the bear- 
ings of FG and GG' : the angle at 

G' from the bearings of GG'and FG'; and the angle at F from the 
bearings of FG and FG'. There are given then the three angles 
of the triangle, and the length of one side, from which can be 
calculated the lengths of the other sides. 

Case 4. When, the hearings ofttoo sides are wanliug. 

((/) AVhen the deficient sides ad.toin each OTHER. In Fig. 
IK), find the length and bearing of DF as before. Then, in the 
triangle DEF, there are given the lengths of the three sides, from 
which can be calculated the required angles. 

(J) When the deficient sides are separated from each 
OTnEii. In Fif. 11.5, let the bearings of CD and GF be wanting 
Calculate the length and bearing of FG' as before. Then, in the 




>e: 



.1 If.. 



1(50 



PLANE SUKVEYING 



triaiicrlii F(t(t', there are tbree sides known, from which can be cal- 
culated the three angles, and therefore the bearings can be deduced. 

UNITED STATES PUBLIC LAND SURVEYS. 

The first survej-s of the public lands of the United States were 
carried out in Ohio, under an act of Congress approved May 20th, 
17S5. This act provided for townships 6 miles square, containing 
36 sections of 1 mile square. The townships G miles square, were 
laid out in ranees, extending northward from the Ohio Eiver, the 
townships being numbered from south to north, and the ranges 
from east to west. The territory embraced in these early surveys 
forms a part of the present state of Ohio and is known as "The 
Seven Ranges." The sections were numbered from 1 to 36 com- 



N 



/V 



W 



36 


30 


24 


16 


12 


6 


35 


29 


23 


17 


1! 


5 


34 


28 


22 


16 


10 


4 


33 


27 


21 


15 


9 


3 


32 


26 


20 


14 


e 


2 


31 


25 


19 


13 


7 


1 



w 



6 


5 


4 


3 


2 


1 


7 


6 


9 


10 


II 


12 


18 


17 


16 


15 


14 


13 


19 


20 


21 


22 


23 


24 


30 


29 


26 


27 


26 


25 


31 


32 


33 


34 


35 


36 



5 vS- 

Fig. 117. " Fig. 118. 

menciiig with No. 1 in the auuthiiist corner of the township, and 
runniui' from Kimth to nurth in each tier, to No. 36 in the north- 
west corner of the townships as shown in Fig. 117. 

A subsequent act of Congress, approved May iSth, 1796, pro- 
vided for the appointment of a surveyor general, and directed the 
survey of the lands northwest of the Ohio Hiver, and above the 
mouth of the Kentucky Eiver. This act provided that " the sec- 
tions shall be numbered respectively, beginning with the number 
one in the northeast section, and proceeding west and east alter- 
nately, through the township, with progressive numbers till the 
thirty-sixth be completed." This method is shown in Fig. 118 
and is still in use. 

An act of Congress, approved Feb. 11th 1805, directs the sub- 
division of the public lands into (juarter sections, and provides that 




a I 



&:i 



S?3 
11^ 






P O I 

S ^ o 

rs-9 

d3u 

OJ y; d 

p.a,g 



n «- 2 



a o'C 

"Is 

- «^ M 

c t n 

se 



PLANE SURVEYING 161 

all the corners marked in the public surveys shall be established 
as the proper corners of sections, or subdivisions of sections, which 
they were intended to designate, and that coiners of half and 
quarter sections not wnrhed shall he placed, as nearly as possible, 
••equidistant from those two corners which stand on the same line." 
This act further provides that '• the boundary lines actually mm 
and marked ''^ * "'^ shall be established as the proper bound- 
ary lines of the sections or subdivisions for which they were 
intended; and the leno-th of such lines as returned by •'■ * * 
the surveyors * * ''' shall be held and considered as the 
true length thereof " 

An act of Congress, approved April 2-lth, l.S~G, provides for 
the sale of public lands in half-quarter sections, and requires that 
••in every case of the division of a quarter section the line for the 
division thereof shall run north and south. An act of Congress, 
approved April 5th, 1832, directed the subdivision of the public 
lands into quarter-quarter-sections and that in every case of the 
division of a half-quarter section, the dividing line should run 
east and west; and that fractional sections should be subdivided 
under rules and regulations ])rescribed by the Secretary of the 
Treasury. 

By an act of Congress, approved March ord, 1S49, the Depart- 
ment of the Interior was created, and the act provided "That the 
Secretary of tlie Interior shall perform all the duties in relation to 
the General Land Office, of supervision and appeal now discharged 
by the Secretary of the Treasury. * * *" By this act the 
Genej-al Land Office was transferred to the Dejiartment of the 
Interior where it still remains. 

The division of the public lands is effected by means of merid- 
ian lines and parallels of latitudes established six miles apart. 
The squares thus formed are called Toicnsliips, and contain 36 
square miles, or 23,040 acres '• as nearly as may be. " All of the 
townships situated north or south of each other, form SiJiamje and 
are named by their number east or west of the principal meridian. 
Thus, the first range west of the meridian would be designated as 
Range 1 "West (R 1. W.). Each tier of townships is named by 
its number north or south of the base line, as Township 2 North 
(T. 2. N.j. 



162 PLANE SURVEYING 

Existing laws further require that each township shall be 
divided into thirty-six sections, ]>j two sets of parallel lines, one 
o-overned by true meridians and the other by parallels of latitude, 
the latter intersecting the former at right angles, at intervals of 
one mile ; and each of these sections must contain, as nearly as 
possible, six hundred and forty acres. These requirements are 
evidently inconsistent because of the convergency of the meridians, 
and the discrepancies -will be greater as the latitude increases. 

In view of these facts, it was provided in section 3 of the act 
of Congress approved MaylOth, 1800, that "in all cases where the 
exterior lines of the townships, thus to be subdivided into sections 
and half-sections, shall exceed, or shall not extend six miles, the 
excess or deficiency shall 1)6 specially noted, and added to or 
deducted from the western or northern ranges of sections or half- 
sections in such township, according as the error may be in running 
lines from east to west, or from south to north ; the sections and 
half-sections bounded on the northern and western lines of such 
townships shall be sold as containing only the quantity expressed 
in the returns and plots, respectively, and all others as containing 
the complete legal quantity." 

To harmonize these various requirements as fully as possible, 
the following methods have been adopted by the general land office. 

Initial points are first establis bed astronomically under special 
instructions, and from this initial point a " principal meridian " is 
laid out north and south. Through this initial point a "base 
line" is laid out as a parallel of latitude miming east and west. 
On the principal meridian and base lines, the half-mile, mile and 
six-mile corners are permanently located, and in addition, the 
meander corners at the intersection of the line with all streams, 
lakes or l>ayou3 prescribed to be meandered. These lines niay be 
run with solar instruments, but their correctness should be checked 
by observations with the transit upon Polaris at elongation. 

Standard parallels, also called correction lines, are run east 
and west from the principal meridian at intervals of twenty-four 
miles north and south of the base line, and the law provides that 
"where standard parallels have been j)laced at intervals of thirty 
or thirty-six miles, regardless of existing instructions, and where 
gross irregularities require additional standard lines, from which to 



PLANE SURVEYING 1(53 



initiate new, or npou which to close old surv^eys, an intermediate 
correction line should be established to which dlooal name may be 
oiven: and the same will be run, in all respects, like the regular 
standard parallels."' 

Guide meridians are extended north from the base line, or 
standard parallels, at intervals of twenty-four miles east and west 
of the principal meridian. 

"When conditions are such as to require the guide meridians 
to run soulli from a standard parallel or a correction lint^, they are 
initiated at properly established closing corners of the giv^en paral- 
lel. That is to say, they are begun from the point on the parallel 
at which they would have met it if they had been run noHh from 
the next southern parallel. This point is obtained from computa- 
tion, and rs less than twenty-four miles from the next eastern or 
western meridian by the convergence of the meridians in twenty- 
four miles. 

In case guide meridians have been improperly located too far 
apart, auxiliary meridians may be run from standard corners, and 
these may be designated by a local name. 

The angular convergence of two meridians is oi\ren by the 
equation 

= m sin L {!) 

where m is the angular difference in longitude of the meridians, 
and L is the mean latitude of the north and gouth length under 
consideration. 

The linear convergence in a given length I is 

c = ^ sin (^ (3) 

The radius of a parallel at any latitude L is given by the 
equation 

r = cos L (3) 

where R is the mean radius of curvature of the earth. 

The distance between meridians is usually given in miles and 
this must be reduced to degrees. To do this it is first necessary to 
hnd the linear value of one degree of longitude at the mean latitude 
from the proportion. 

1^ : 360" : : a' : 2n>' (4) 

the value of /• being found from (3) 



164 PLANE SURVEYING 



Equation (4) will give results sufficiently accurate, although 
in strict accuracy R Bhould be the radius of curvature at the mean 
latitude. 

For full details of public-land surveying, see " Manual of 
Surveying Instructions for the Survey of the Public Lands of the 
United States," issued by the Commissioner of the General 
Land Office. These '■ Instructions" are prepared for the direction 
of those engaged on tiie j)ublic land surveys, and new editions are 
issued from time to time. 

Much of the foregoinij in ver-^- comlcnsed form is taken from 
the edition of 1894. 

Tlie following table gives the convergency both in angular 
units and linear units for township!) miles S(]uare. between lati- 
tudes 30 and 70' north. 

Lt«t it be re(]uired to tiiid from tLie table the linear converg- 
ence for a township situated in latitude 38 29' north. 

Looking in the talile opposite 39 we find the linear con- 
vergence. 

For 39° = 58.8 links 

For 38' = 5<).8 .links 

Difference for 1° = 2.0 links 
Difference for 1' = 2.0 -^ 00 = .0333 links 
Difference for 29' = .0333 X 29 = .97 links 

Therefore total convergence for latitude 38° 29' := 56.8 -f- 
0.97 links -^ 57.77 links. 



PLANI-: SrRVF.VTXi; 



BASE riEASL'REnENT. 

Itis not inteniled in what follows to go info the details of the 
measurement of a base for an extended system of triangulation, as 
that properly belongs to Geodetic Surveying. Some descrijition 
of base measuring apparatus will lie given, with illustrations of 







Jonvergcncs 




Lat. 


Coiivorgency 


Lat. 














On the 


.Vn 






On the 


Ansle. 




Parallel. 




l)p;rri-i\.i. 


Parallel. 


Deirrces. 


Liuk.<. 


Minutes. 


Si»coik1s. 


Link."!. 


Minutes. 


Secoi.d>. 


30 


41.9 


3 





50 


86.4 


6 


12 


31 


43.6 


3 


7 


51 


89.6 


6 


25 


32 


45.4 


:! 


15 


52 


92.8 


n 


.39 


33. 


47.2 


.3 


23 


53 


96.2 


(i 


54 


34 


49.1 


.3 


.30 


54 


99.8 


7 


9 


35 


50.9 


:; 


3.S 


55 


ia3.5 


7 


25 


3G 


52.7 


3 


40 


56 


107.5 


y 


42 


37 


54.7 


:! 


5."! 


57 


111.6 


,s 





38 


56.8 


4 


01 


58 


116.0 


S 10 


.39 


58.8 


4 


13 


59 


120.6 


S .38 


40 


60.9 


4 


•)•> 


CO 


125.5 


8 59 


41 


&3.1 


4 


.31 


61 


130.8 


9 22 


42 


65.4 


4 


41 


62 


136.3 


9 46 


43 


67.7 


4 


51 


63 


142.2 


10 11 


44 


70.1 


5 


1 


64 


148.6 


10 38 


45 


72.6 


5 


12 


65 


1.55.0 


11 8 


46 


75.2 


5 


•>:i 


66 


162.8 


11 39 


47 


77.8 


5 


z^ 


67 


170.7 


12 13 


48 


80.6 


5 


4() 


68 


179.3 


12 51 ■ 


49 


a3.5 


5 


59 


69 


188.7 


13 31 










70 


199.1 


I 1 


!."» 



various devices, and special attention will be given to tlio use of 
the tape in the accurate measurement of lines such as occur in usual 
field operations of Plane Surveying. 

Much of what follows is from the excellent treatise on Topo- 
graphic Surveying by Herbert M. Wilson. 

A trigonometric survey is usually carried over a country where 
the direct measurement of distances is iinjiracticable, and since the 
calculations of these distances proceeds from the direct measure- 
ment of the base-line, this base line should be so located as to 
permit of its length being determined with any degree of accuracy 
consistent with the nature of the work involved. 

To attain the desired results, the site should be reasonably 
level and afford room for a base of proper length so that its ends 
may be intervisible. and permit of the development of a scheme of 



166 



PLANE SURVEYING 



primary triangulation giving the best-conditioned figures possible. 
Other things being equal, that site is best that includes solid 
ground; both for permanency of monuments and facility and 
accuracy of measurement. 

Base Apparatus. In early days, base-lines were measiired by 
means of wooden rods, varnished and tipped with metal. The rods 
were supported in trestles, the contacts between the ends being 
made with great care. Later, compensated rods were employed, aa 
for instance the Contact-Slide Apparatus of the U. S. Coast Survey 
and the Ilepsold primary base bars of the U. S. Lake Survey, see 
Fig. 119, resulting in greater accuracy in the measurement of base 
lines. The use of the iCed lar (see Fig. 120) by the U. S. Coast 
Survey, represents the highest development of base-measuring 
apparatus. 




■•^v^'^^'fUgI'^»'^' 



Fig. 119. 

Within recent years the steel fajie has becoule popular as the 
accuracy attainable with its use has become more fully appreciated. 

Errors in Base rieasurement. The following are the chief 
sources of error m base measui-ement: 

1. Changes of temperature ; 

2. Difficulties of making contact ; 

.3. Variations of the bars or tape from the standards. 

The refinements of measurement consist especially in — 

a. Standardizing the measuring apparatus, or its comparison with a 
standard of lengtn. 

h. Determination of temperature, or its neutralization by the use of 
compensating bars. 

c. Means adopted for reducing the number of contacts to the fewest 
possible, and of making these with the greatest degree of precision. 



PLANE SUKVEYIXG 



167 



The inherent difficulties of lueaL.ureinent wltli htrs of any 
kind are : 

1. Necessity of measuring short bases because of the number of times 
which the bar must bo miivod. 

2. Expense, as a considerable number of men are required. 

3. Slowness, the measurement often occupying from a month to six- 
weeks. 

The advantaijes of measurement made witli a steel tape aro : 

1. Great reduction in the number of contacts, as the tapes are about 
three hundred feet long as compared with bars of about twelve feet. 

2. Comparatively small cost because of the few per.sons reiiuired. 

3. Shortness of the time employed, an hour to a mile being an ordinary 
record in actual measurement 

4. Errors in trigonometric e.vpansion may be reduced by increasing the 
length of the base from 5 miles, the average length of a bar-mea.sured base, 
to 8 miles, not an uncommon length for tape-measured bases. 




Fig. 1-20. 

Steel tapes offer a means of measuring base lines wliicli is 
superior to that obtained by measuring bars, because they combine 
the advantages of great length and simplicity of manipulation, 
with the precision of the shorter laboratory standards, providing 
only that means be perfected for eliminating the errors of tem- 
perature and of sag in the tape. Base lines can be so conveniently 
and rapidly measured with long steel tapes as to permit of their 
being made of greater length than has been the practice with lines 
measured by bars, and as a result, still greater errors may be 
introduced in tape-measured bases and yet not affect the ultimate 



168 



ILANE SURVEYING 



expansion any more than will tlie errois in the latter, because of 
the greater leiitfth of the base. 

The ta|ies used for this work are of steel, either 300 feet or 
100 meters in length. The tapes used by the Coast Survey are 
101.01 meters in length, O.Sd millimeters by 0.47 millimeters in 
cross-section, and weigh 22.3 grams per meter of length. They are 

subdivided into 20 meter spaces 
by graduations ruled ow the sur- 
face of the tape, and their ends 
terminate in loops obtained 
either by turning back and an- 
nealing the tape on itself, or bv 

fastening them into brass hand- 
ed 

les. When not in use, the tapes 
are rolled on reels for easy trans- 
portation. 

The steel tapes used by the 
Geological Survey, are similar to 
those used by the Coast Survey, 
excepting in their length, which 
is a little over i500 feet. They 
are graduated for 800 feet and 
are subdivided every 10 feet, the 
last 5 feet of which at either end 
is subdivided to feet and tenths. 
The various instrument-makers now carry such tapes in stock, 
wound on hand -reels. All tapes must be standardized before and 
after use, by comparison with laboratory standards, and, if possible, 
thereafter fre(piciitly in the Held by means of an iced-ljar ap{)aratus. 
In measuring witli steel tapes, a uniform tension must Ije 
applied. In order to get a uniform tension of 20 to 25 pounds, 
some form of stretcher should be used. That used by the I'.S. 
Coast Survey consists of a base of brass or wood, 2 or 3 feet 
in length by a foot in width, upon which is an upright metallic 
standard, and to this is attached liy a universal joint, an ordinary 
spring-balance, to which the liaiidle of the tape is fastened. See 
Fig. 121. The upright standard is hinged at its junction with 
the base, so that when the tape is being stretched, the tapeman 




Kit,'. 1-Jl. 



PLANE SUEVEYIXG 



169 



1^ 



V^. 



^ 



1 



>:S 



^I 



S^ 






=^ 



^ '^ 



J3 s 



:.:- M 



170 PLANE SUKVEYING 

can put the proper tension on it by taking hold of the upper end 
of tlie uiiright standard and using it as a lever, and by pulling it 
back toward himself he is enabled to use a delicate leverage on the 
balance and attain the proper pull. 

The thermometers used are ordinary glass thermometers, 
around the bubbles of which should be coiled thin annealed steel 
wire, so that by passing them in the air adjacent to the tape, a 
temperature corresponding to that of the tape can be obtained. 
Experience with such theriiioiiieters shows that they closely fol- 
low the temperature of the steel tape. For 
the best results, two thermometers should 
be used, each at about one-fourth of the 
distance from the extremities of the tape. 
The stretching device used by the U. S. 
Geological Survey is much simpler and 
more quickly manipulated than that of the 
Coast Survey. The chief object to be at- 
tained in tension is steadiness and uni- 




Fig. 12:?. formity of tension; the simplest device 

which will attain this end is naturally the 
best. Twu general forma of such devices are employed by the U . S. 
Geological Survey, one for the measurement of base lines along 
railways, wliere the surface uf the ties or the roadbed furnishes 
support for the tape, and the device must therefore be of such 
kind as to permit of the ends being brought close to the surface; 
the other is employed in measurements made over rough ground, 
where the tape may frequently be raised to considerable heights 
above the surface and be supported upon pegs. 

The stretcher used by the Geological Survey for measuring 
on railways is illustrated in Fig. 122, and was devised by Mr. H. 
L. Baldwin. It consists of an ordinary spring-balance attached to 
the forward end of the tape, where a tension of twenty jiounds is 
applied, the rear end of the tape being caught over a hook which 
is held steadily by a long screw with a wing-nut, by which the 
zero of the tape may be exactly adjusted over the mark scratched 
on the zinc plate. The spring-balance is held by a wire running 
over a wheel, which latter is worked by a lever and held by 
ratchets in any desired j)Osition, so that by turning the wheel, a 



PLANE SUKVEYING 171 



uniform sti'ain is placed on the spring-balance, which is held at 
the desired tension by the ratchets. 

The tape-stretcher used by the U. S. Geological Survey off 
railways consists of a board about 5 feet long, to the forward end 
of which is attached by a strong hinge, a wooden lever about 5 
feet in length, through the larger portion of the length of which 
is a slot. See Fig. 1'2'i. Through the slot is a bolt with wing- 
nut, which can be raised or lowered to an elevation corresponding 
with the top of the hub over which measurement is being made; 
hung from the bolt is the spring-balance, to which the forward 
tapeman gives the proper tension by a direct pull on the lever, 
the weight of the lever and the friction in the hinge being such as 
to make it possible to bring about a uniform tension without dif- 
ficulty. The zero on the rear end of the tape is adjusted over the 
contact mark on the zinc by means of a similar lever with hook- 
bolt and wing-nut, but without the use of spring-balance. 

Laying out the Base. The most laborious operation in base 
measurementis its preliminary preparation, which consists of: 

1. Aligning with transit or theodolite; 

2. Careful preliminary measurement for the placing of stakes on rough 

ground; 

3. Placing of zinc marking-strips on the stakes. 

Base lines measured with steel tapes across country are aligned 
with transit ortheodolite, and are laid out by driving large hubs 
of 3 X *) scantling into the ground, the tops of the same project- 
ing to such a height as will permit a tape-length to swing free of 
obstructions. These large hubs are placed by careful preliminary 
measurement at exact tape-lengths apart, and between them as sup- 
ports, long stakes are driven at least every 50 feet. Into the sides 
of these near their tops are driven horizontally, long nails, which 
are placed at the same level by eye, by sighting from one terminal 
hub to the next. The tape rests on these nails and on the surface 
of the terminal hubs are tacked strips of zinc on which to make the 
contact marks. A careful line of spirit-levels must be run over 
the base-lines, and the elevation of the hub or contact-mark of each 
tape-Jength must be determined in order to furnish data for 
reduction to the horizontal. 

In measuring over rough ground, six men are necessary: two 
tape- stretchers, two markers, two observers of thermometers, one 



172 PLANE SURVEYING 

of whom will record. The co-operation of these men is ol)tained 
by a code of signals, the first of which calls for the application of 
the tension; then the two tape-stretchers by signal announce when 
the proper tension has been applied; then the rear observer adjusts 
the rear graduation over the determining mark on the zinc plate 
and gives a signal, upon hearing which, the thermometer recorder 
neartlie middle of the tajje lifts it a little and lets it fall on its 
supports, thus straightening the tape. Immediately thereafter the 
fi'ont t)bserver marks the position of the tape graduation on the 
zinc plate, and at the same time the thermometers are read and 
recorded. 

After the measurement of the base line has been completed in 
the tield, the results of the measurement have to be reduced for 
various corrections, among whicli are: 

Comparison with standard measure; 

Corrections for inclination and sag of tape if such is used; 

Correction for tenii)erature. 

The first correction to be applied is that of reducing the tape- 
line to the standard, "standardizing"' the tape as it is called. By 
sending the tape to the National Bureau of Standards at Washing- 
ton, I). (".. a statement may be had of the length of the taiie com- 
pared with the standard. For this service a small fee is charged. 
For an additional fee a statement may l)e had of the temperature 
and pull at the ends for which the tape is a standard. 

As the length of a steel tape varies with the temperature, one 
of the most uncertain elements in the measurement of a base with 
the steel ta])e, is the change in the length of the standard due to 
changes of temperature. Corrections, therefore, must be made for 
every tape-length as derived from readings of one or more ther- 
mometers applied to the tape in the course of measurement. 

Steel expands .()()0()0():55iJ() of its length for each degree 
Fahreidieit. This decimal multiplied by the average nuTuber of 
degrees of temperature above or below 02 degrees at the time of 
the measurement, gives the projwrtion by which the base is to be 
diminished or extended on account of temperature changes. This 
correction is applied usually by obtaining witli great care, the 
mean of all thermometer readings taken at uniform intervals of 
distance during the measurement. 



PLANE SURVEYING 173 

The data for the correction for incliiiiition of base are obtained 
bv a careful line of spirit-levels over the base-line. In the course 
of this leveling, elevations are obtained for every plug upon which 
the tape rests. The result of this leveling is to give a profile 
showing rise or fall in tVet or fiactions thereof between the points 
111' change in inclination of the tape-line. From this and measured 
distances between these points, the angle of inclination is com- 
jiutcd by the formula 

sin 4> = ^'^ 

111 which 1> is the length of the tajie or measured base : 

and /* is the difference in height of the ends of tape or 

measured base, expressed in feet. 

4> is the angle of slope expressed in minutes. 

The correction in feet to the distance is that computed by the 

equation 

„ sin- 1' .., 
Correction = IJ 6- 

An <ij)p)ui:riiit(it<' formula for reducing distances measured 
upon slojiing ground to the horizontal is expressed by the rule : 
Divide the square of the difference of level by twice the measured 
distance, subtract the quotient thus found from the measured 
distance, and the remainder equals the distance required ; thus 



2D 



in which </ equals the horizontal or reduced distance. 

When the l)ase measurement is made with steel tape across 
country, and accordingly is not supported in every part of_ its 
length, there will occur some change in its leno'th, due to sag. As 
previoxxsly explained, the tape should be rested upon supports not 
less than 50 feet apart. With supports placed even this short dis- 
tance apart, however, a change of length will occur between them, 
while even greater changes will occur should one or more supports 
be omitted as in crossing a road, ravine, etc. Since tapes are 
standardized by laying them upon a flat standard, it is necessary 
to determine the amount of shortening from the above causes. 



174 PLANE SURVEYING 



The following ivduction formulaj apply : 

Let "' ^ weight j)er unit of length of tape : 
t = tension aj.plied 

w 
""= — 
n = number of sections into which tape is divided by 

supports. 
I = length of any section 

L = normal length of tape or right-line distance be- 
tween n marks when under tension : = ul ap- 
proximately. 
If a tape be divided by equidistant supports, the difference in 
distance between the end graduations, due to sag, or the correction 
for sacr = i/L becomes 

If (ine or more supports are omitted, then the omission of w 
consecutive supports shortens the tape by 

^l^-/,, {>a + 1) {m + 2) u'P: 

when / is the length of the section when no supports are omitted. 
E.rairiji/e. Let n — G ; f ^= 50 feet ; /" =. .0145 = weight 
in pounds per foot found l>y dividing whole weight of tape by 
whole length ; < = 20 pounds. 

,l^J± (mix = 0.0162 feet, 
24 t 

which is the amount of shortening of each tape-length. This cor- 
rection is always negative. 

If there had been 80 full tape-lengths in measured l>ase-line. 
the total corrections for sag would be S6 X .01(32 = 1.393 feet. 

THE PLANE=TABLE. 

Construction. The y)lane-table consists essentially of a draw- 
ing-board imuiiited upon a tripod. This board is usually twenty- 
four by tliirty inches, constructed in sections to ])revent warping; 
it is attached to the tripod by a three-screw leveling base arranged 



PLANE SURVEYING 175 



to permit the board to he turned iu aziiiiutli and to be clamped in 
any position. 

The instrument is designed to at onee sketch in the field, to 
scale, the lengths and relative directions of all lines and the posi- 
tions of objects to be included in the survey. For drawing 
straight lines, a steel ruler is provided upon which is mounted at 
each end, a pair of open sights like those of the couipass, or, a tele- 
scope is mounted at the center of the ruler, fitted with stadia 
wires, a vertical arc and a longitudinal striding level. The eye- 
piece should be inverting, and whether the open sights or the tele- 
scope is used, the line of sight shoTild always be parallel to the 
edge of the ruler. The straight edge with the, attached telescope 
or open sights is called the 'd'ulihlc. 

For leveling the instrument, two cylindrical levels, at rii^ht 
angles to each other, are mounted upon the alidade and either an 
attached or detached compass is ])rovided for determining the bear- 
intr of lines. 

o 

For attaching the paper to the board, various devices are 
used. One consists of a roller at each end of the table u])on one 
of which the paper is wound up as it is unrolled from the other, 
the edges of the paper being held close to the board by sprino- 
clips. This arrangement permits the paper to be used in a con- 
tinuous roll and to be tightly stretched over the board. The use 
of the continuous roll of paper is iindesirable, however, and 
separate sheets of proper size should be used, attached to the board 
and held firmly in place by the spring clips provided with the 
instrument. The use of thumb-tacks should be avoided. 

Under the most favorable conditions, the plane-table is a very 
awkward instrument and difficult to handle, but it is admirably 
adapted to filling in the details of a topographical survey. For this 
purpose it is the standard instrument of the United States Geo- 
detic Survey and is also largely used by the United States Geolog- 
ical Survey. It cannot be used oh damp or very windy days and is 
not therefore, of as general utility as the transit and stadia. 

Fig. 124 shows one form of construction of the plane table 
with leveling screws and Fig. 124« shows a plane table with a much 
simpler form of leveling head. This latter was designed by Mr. 
W. D. Johnson and has received the approval of the topographers 



176 



PLANE SURVEYING 



of the T'nited States Geological Survey. The. whole arrangement 
is very light, but does not permit of as close leveling as does the 
usual form -with levelincr screws. 

Adjustments. 

1st. Til dtfermvne whether the edge of the ruler -is straii/ht. 




Fig. 124. 

Place the ruler upon a smooth surface, and draw a line along its 
edge, and also lines at its ends, lleverse the ruler on these lines, 
and draw another line along its edge. If these two lines coincide, 
the ruler is straitrht. 



PLANE SirKVEYrNC4 



m 



2nd. To maJie the jilaiic of the tahle horizontal when the 
hubhles are in the center of the tiihea. Assuming the table to be 
plane, set the alidade in the middle of the table, level by means of 
the leveling screws, draw lines along the edge and ends of the 
ruler, and reverse the alidade on these lines. Il" the bubbles 
remain in the center of thr tnb('s, they are in ad justment. Tf they 







Fifr. 124«. 

do not, correct one-half of the error l)y means of the leveling 
screws and the remainder by means of the capstan -headed screws 
of the level tubes. Repeat the operation until the bubbles remain 
in the center of the tubes in both positions of the alidade. 

3rd. To inali'e the line of collirnation perpend icidar to the 
horizontal axis of the telescope. 



178 tLANE SURVEYIXG 

Level the table and point the telescope towards some small 
and well-defined object. Remove the screws which confine the 
axis of the telescope in its bearings, reverse the telescope in its 
bearings, that is, change the axis end for end, being careful not to 
disturb the position of the alidade upon the table, and again sight 
upon the same object. If the intersection of the cross hairs bisects 
the object, the adjustment is complete. If not, correct one-half 
of the error by means of the horizontal screws attached to the 
reticle. Sight on the object again and repeat the operation until 
the line of collimation will bisect the object in both positions of 
the telescope. 

4th. To mull- till' line of cnl] iniatioii jiarnlhl to tJie (i.rix/if 
the bubble tube. 

Attach the longitudinal striding level to the telescope and 
carry out the adjustment by the '• peg " method as described for 
the transit. 

5th. To make the hnrisontaJ ii.r'inoftheiehxropcjiiir'ilhlto 
the phtne of the table. 

Level the table and point the telescope to a well-defined mark 
at the top of some tall object, as near as possible consistent with 
distinct vision. Turn the telescope on its horizontal axis, and 
point to a small mark at the base of the same object. Draw 
lines on the table at the edge and ends of the ruler. Reverse 

o 

on these lines, point the telescope to the lower object and turn the 
telescope upon its horizontal axis. If the line of collimation again 
covers the higher point, the adjustment is complete. If it does 
not, correct one-half of the error by means of the screws at one 
end of the horizontal axis. 

0th To make the vertical ore or rircle reoil zero uihcii the 
line of collhiiiition is horizontiil . 

Level the table and measure the angle of elevation or depres- 
sion of some object. Ileraove the table to the object, level as 
before, and measure the angle of depression or elevation of the 
first point Half the difference, if any, of the readings is the 
error of the adjustment. Correct this by means of the screws 
attached to the vernier plate, and repeat the operation until the 
angles as read from the two stations are equal. 



PLANE SDKVEYING 



179 




Fig.i-J 



Use. The plaue-table is used for the immediate mapping of 
a survey made with it, no angles being measured, but the direction 
and length of lines being plotted at once, upon the pa])er. The 
simplest ease is the location of a number of points from one centi-al 

point, called the method of radi- 
ation. The table is "set up" so 
that some convenient point upon 
the paper is over a selected spot 
upon the ground and is then 
clamped in azimuth. Mark the 
point upon the table by sticking a 
needle into the board. Now bring 
the edge of the alidade in contact 
with the needle and swing it 
around until the line of sicrht, 
which is parallel to the edge of the ruler, is directed to the point to 
be located. Having determined the scale of the j)lat, aline is drawn 
along the edge of the ruler to scale, equal to the distance to the 
desired point, such distance having been measured either with the 
tape or stadia. In the sanie way locate all of the other points, 
which may include houses, trees, river banks, etc. If the plane- 
table is set up in the interior of a field at a point from which all 
of the corners are visible, the corners can lie thus located and after 
being connected, there results a 
plot of the area. Instead of occu- 
pying a point in the interior of the 
iield, one corner may be selected 
from which all of the others are 
visible, or a point outside of the 
field may be chosen from which to 
measure the lines to the several 
corners. Evidently fi'om such a 
survey, data is lacking from which 
to calculate the area, and either 
the map must be scaled for addi- 
tional data or the area measured with the planimeter. 

The Fig. 125 illustrates the method of surveying a closed 
area by the method of radiation. The plaue-table is at the point 




Fig. 126. 



180 



PLANE SURVEYING 




o and drawn to an exaggerated scale. The area aljcd<- representing 
to scale, the area ABODE. It may be desirable to set up the 
table at some other point, as for instance one of the corners of the 
field, and run out some of the lines to the other corners as a check 
upon tile work. 

Traversing, or the Method of Progression. This method is 
practically the same as the njethod of surveying a series of lines 
with the transit, but requires that all of the points be accessible. 
It is the best method of working as it provides a complete check 
upon the survey. 

Let ABODE, Fig. 12(],l.e the 
series of lines to be surveyed by 
tvtivcrfdng. Set up the table at 
B, the second angle of the line, 
so that the point h upon the paper 
will be directly over the point 
15 I'jion the ground. (The point 
h should be so chosen as to leave 
room upon the pajjer for as much 
of the traverse as possible.) Stick 
a needle at the point Tj and place 
the edge of the alidade against it. Swing the alidade around until 
the line of sight covers the point A. Measure BA and lay it off to 
the proper scale as ha. Now turn the alidade around the point h 
iind sight to and measure the distance BO and plot it to scale as he. 
Iiemove the instrument to c with the point r upon the paper directly 
over upon the ground, and '•/> in the direction of CB. Thisisdifii- 
cult to accomplish with the plane-table, but if the plot is drawn to 
a large scale, it must be done. If the plot is drawn to a small scale, 
it will be sufficiently accurate to set the table over the point C as 
nearly as possible in the proper direction and then turn the hnard 
in azimuth until h is in the direction of B. Stick a needle at r. and 
check the length of rfi. Swing the alidade around c until the line 
of sight covers D, measure CD and plot cd. Remove to D and 
proceed as before and so on through the traverse. 

If the survey is of a closed field, the accuracy of the work 
will be checked by the closure of the survey. 



I 



Fig. 127. 



PLANE SURVEYING 18J 

The method of progression is especially adapted to the survey 
of a road, the banks of a river, etc., and often many of the details 
may be sketched in witli the eye. 

AVhen the paper is filled, put on a new sheet, and on it, lix 
two points, such as D and E, which were on the foririer sheet and 
fioin them proceed as before. The sheets can afterward he united 
so that all points on both shall be in their true relati\e positions. 

riethod of Intersection. This is the most raj>id method of 
using the plane-table. Set up the instrument at any convenient 
point, as A in Fig. 127 and sight to all the desired points as D.E, 
F, etc., which are visible, and draw indefinite lines in their direc- 
• tions. Measure any line as AB, B being one of the points sighted 
to, and [)lot the length of this line upon the pa[)er tu any convenient 
scale. Move the instrument to B so that h upon the pajier will be 
directly over B lipon the ground, and so that hn upon the paper 
will be in the direction of BA upon the ground as e.xplaiiied under 
the method of progression. Stick a needle at the point l> and 
swinii- the alidade around it, sijrhtiuji to all the former i)oints in 
succession, and draw lines in their direction. The intersection of 
these two sets of lines to the several points will determine the 
position of the points. Connect the points as <l, fi,f\ (j, in the 
figure. In surveying a field, one side may be taken as the base 
line. In choosing the base line, care must be exercised to avoid 
very acute or obtuse angles: 30° and 150^ being the extreme limits. 
The ini possibility of always doing this, sometimes renders tins 
method deficient in precision. 

TOPOGRAPHICAL SURVEYING. 

A topographical map is one showing the configuration of the 
surface of the ground of the area to be mapped and includes lakes, 
rivers, and all other natural features, and sometimes artificial 
features as well. 

A topographical survey is one conducted for the purpose of 
acquiring information necessary for the production of a topograph- 
ical map of the area surveyed. 

Nearly all engineering enterprises involve a tojiographical 
survey more or less extended, depending upon the nature and 



182 PLANE SURVEYING 



importance of the contemplated work. The construction of an 
important building may involve a survey of the foundation site 
to determine the amount of cut and fill ; the construction of a 
bridge will involve a hydrographic survey of a body of water to 
ac(juire information in regard to direction and velocity of current, 
depth of water, nature of bottom, and pro])er site for piers and 
aliutments. A jiroposed railroad will not only involve a survey 
of the line itself, but a tO{)Ographical survey extending from 200 
to 400 feet upon each side. The design of a sewer system or a 
waterworks system, dams, reservoirs, canals, irrigation channels, 
tunnels, etc , all involve topographical surveys. 

In what follows it is intended to outline the methods of con- 
ducting field operations, based partly upon the nature and impor- 
tance of the problem involved, and partly upon the instruments 
used. The ditfereiit methods of representing topography and the 
involved drafting-room work will be fully treated in Topographical 
Drawing. 

The field opeiatioiis, in so far as the methods and instruments 
are concerned, may l)e classified as follows : 

1. Sketching; by the eye, without or v.ith the tape for measuring dis- 
tances. 

2. Sketching with the aid of the Locke hand-level or clinometer, hori- 
zontal distances Ijoing measured either by pacing or with the tape. 

3. Deti'rmining the elevation of points with the wye-level, horizontal 
distances being determined either with the stadia or tape. 

4. Determining points with the transit and stadia. 

5. Topographical .sketching with the plane-table and stadia. 

6. Photogra[)hy. 

7. Triangulation. 

It is evident that the first method is entirely lacking in accu- 
racy, and such work should be done only when speed is the most 
important consideration, only the roughest approximation to the 
topographical features being attempted ; contour lines cannot be 
located. Work of this nature is of value principally for purposes 
of promoting an enterjirise ; artistic, showy plates being desired. 
Little can be said descriptive of the manner of carrying out the 
6eld work, since this will require considerable artistic ability as 
well as the ability to "see" things and est'jiate distances. Com- 
paratively few men ])ossess the aliility to carry out topography of 
this nature. It necessarily follows tliat the wurk must be done 



PLANE SURVEYING 183 



entirely by sketching in the field, and for this purpose the 
following equipment is needed : 

2 or 3 medium pencils, kept well sharpened. 

Rubber eraser. 

Thumb-tacks. 

Several .sheets of drawing paper, 14" X 14". 

One light drawing board, 15" X 15". 

A pocket compass will be useful in determining the bearing 
to prominent objects to tie in the stations of the survey. A Locke 
hand-level or Abney clinometer will also be useful for finding- 
approximate heights, and either of these instruments can be 
readily carried in the pocket. It will be more convenient to have 
the paper cross-ruled into one-fourth inch squares, the center line 
being ruled in red, but if drawing paper is used, it will be neces- 
sary to add an engineer's scale to the etjuipinent. The back of 
the drawing board should be fitted with a leather pocket, with flap 
and button, in which the blank sheets and the finished topographic 
sheets should be kept. A strap attached to the board and to gu 
over the shoulder, will prove a great convenience. A waterproof 
cover should be provided to protect the board and sheets in case 
of rain. 

A compass or transit survey forms the backbone of the topog- 
raphy, and the sketching should include an area upon each side of 
the line so surveyed, and running parallel with it. 

A separate sheet should be used for each course (by course is 
intended the straight line from one turning point to the nextj, no 
matter how short it may be. Begin at the bottom of the sheet 
and sketch the topography up the sheet, that is, in the direction 
of the progress of the survey, and number the sheets in order. 
Begm each new sheet with the same station that ended the preced- 
ing sheet. After the field work is completed, the sheets can be 

laid down in order, the angles between their center lines corre- 
ct 

sponding to the deflection angles as given by the transit notes of 
the survey. The topography can now be traced upon tracing cloth 
in a continuous sheet. The method above outlined will result in 
a saving of time, especially in working up the topographic plat. 

The second method commends itself in connection with a 
preliminary survey of a highway, steam or electric road, irriga- 



184 PLANE SURVEYING 



tion channels, canals, etc. The e(|uij)iiient should be as follows : 

1 or 2 straight edges, about 12 feet in length. 
1 or 2, IIX) foot steel tapes. 
1 or 2 plumb-bobs. 

1 pocket oonipas.s. 

2 or .3 medium pencils, kept well sharpened. 
Rubber eraser. 

Thumb-tacks. 

Several sheets of drawing paper or cross-section paper, 14" X 14". 

One light drawing board, 15" X 15" with waterproof cover. 

The topographic J)arty should be made np of the topographer 
and one or two assistants, depending somewhat u])on the nature of 
the survey and the country traversed. If the country permits of 
rapid progress of the transit and level party, two assistants will be 
necessary to keep the tojuigraphy abreast of the survey. liapid work 
may, however, be done with one assistant, provided the topography 
does not extend more than 200 feet each side of the transit line. 

The iVbney clinometer is well ada])ted for this class of work, 
on account of its portability, which is an important item in a 
rough country with steep side slopes. It can be used in the same 
way as the Locke hand-level, if necessary, but is a more generally 
useful instrument, as is described in Part 1. The straight edge 
should be of well-seasoned, straight-grained material, as light as 
possible, but so constructed as to prevent warping. It should be 
divided into spaces of one foot each, painted alternately red and 
white. The tapes should be of band steel, as they are subjected 
to rough usage, and they should be divided to feet and tenths at 
least. A plumb-bob is necessary for plumbing down the end of 
the tape on steep slopes. The ])Ocket compass is a neremdnj 
adjunct in work of this character. The drawing paper should 
y)referably be cross-section paper ruled into one-fourth inch squares 
with a heavy center line in red, but if ordinary drawing paper is 
used, it will l)e necessary to include in the outfit an engineer's 
scale, by means of which distances njay be j)latted upon the sheet. 
Enough of these sheets should be carried to cover a day's work, but 
no more. The drawing lioard should be fitted up as described 
under the previous method. 

Method of Procedure. The transit line furnishes, of course, 
the backbone of the survey, and the topography will be taken for 



PLANE SURVEYING 185 



thf jiroper disfance upon each side of this line, by locating points 
both as to distance and elevation, upon perpendiculars from the 
transit stations. In rough country, it may be necessary to locate 
these points intermediate between the transit stations. Before 
startinoj out upon a day's work it is necessary to procure from the 
level party, the elevation of the transit stations, or if the topog- 
raphy keeps jiace with the transit survey, the elevation may be ob- 
tained from the leveler at each station. For points intermediate 
lietween transit stations, the elevations may be gotten closely 

enouoh with the clinometer or hand-level. The nuinl)er of each 

IT 

station as well as its elevation, sliould bo noted upon the topo- 
graphic sheet, and the topography will include the location of 
contour lines, at proper vertical intervals, as well as all streams, 
lakes, property lines, etc. An example showing the method of 
keeping the field notes, will at the same time best serve to explain 
the methods of conducting the survey. 

Beoinnino- with station at the bottom of the sheet, the 
11 umber and elevation of the station are noted. See Hof. 128. 
Sendintr the assistant cnit upon one side of the transit line and at 
right angles thereto, he holds the rod at points to be designated by 
the topographer, the distances to be determined by pacing, or with 
the tape, and the elevations determined either by sighting upon 
the rod with the clinometer, or by laying the straight edge upon 
the ground at right angles to the line and applying the clinometer 
to it to determine the slope, from which elevations can at once be 
determined. Contour jioints are then readily interpolated and the 
distance out platted to scale upon the sheet and a note made of the 
elevation of the contour lines. If a lake or stream intervenes 
within the limits of the topographic survey, determine the distance 
to and elevation of the shore line and plat upon the sheet. Deter- 
mine points upon the other side of the transit line in the same way. 

If one or more contour lines cross the transit line between 
stations, determine the points of crossing and plat the points upon 
the sheet, to scale, as shown between stations and 1. It will l)e 
noticed in this case that the elevation of station 0, is 138 feet and 
of station 1, is 141 feet. If contours are to be taken at vertical 
intervals of five feet, it is apparent that the 140-foot contour line 
must cross the transit line between these stations. If the slope of 



186 PLANE SURVEYING 



p E 

-^ F 



Fig. 128. 
the frround is imifonii. tlio point of crossinu; may be taken at two- 
tliiids (if the iiislaiic(! from to 1. ( Hiierwise, locate the point 
with the clindMictcr. 



PLANE SURVEYING 



187 





V 








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'—- 


~N 


6 


















\ 


\ 










1 


^s. 


N 


















vj 


N, 












\ 




















^j 


>-^ 








.^ 


\ 


\ 






















'^ 


--. 


->, 


5 




\ 


^ 
























\ 


\ 








V. 


"^ 






\ 
















\ 














— ■ 




\ 














A 




















\ 












A 


\ 




















\ 








Ul 

z 






\ 


V 
























J 








V, 


N 












j 


\ 










^ 














---, 






J 






M 


^ 


-^ 


3 


















/ 


/ 






























/ 












Q 








^ 


^ 


V 








\ 








] 




UJ 

or 


.^ 










V 


N, 






\ 














2 


f 




-^ 


V 






X 




1 








\ 














^ 


\ 


















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\ 








\ 








\ 




s"^ 




\ 










X 






\ 










\ 


1 




\ 


\, 














\ 


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's 


^ 






V 


\ 














\ 












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s^* 




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C 


3 








D 




o 






u 


1 





145 



140 



Fig. 128. 

Now cro to Station 1 and locate contour points and other 
topographic features as before described, and connect points in the 



188 PLANE SUKVEYING 

same contour line, sketching in the curve of the line with the eye. 
Use a separate sheet for each portion of the transit line from turn- 
ing point to turning point; this will retpiire that the turning 
points apjiear upon two consecutive sheets. Likewise, if the length 
of the line between turning points is too long to be platted upon a 
sincfle sheet, begin the second sheet with the same station that 
completed the first sheet and so continue throughout the survey. 
As each sheet is completed, number it and return to the jiocket on 
the back of the drawing board. The pocket compass should be 
used for determining the bearing of property lines, roads, streams, 
etc., crossed by the survey, and to take the bearings to prominent 
oljjects. 

The topographic sheets should be filed away in such a manner 
as to make them easily accessible at any time, us the engineer in 
charge of the transit survey may wish to consult them from time 
to time. The office work of preparing the topogra[)hic plat can be 
very expeditiously carried out as before described. 

The use of the wye-level as a topographic instrument is 
limited, but for certain kinds of work the instrument is the most 
satisfactory, as for instance, the survey of a dam-site; the survey 
of a reservoir-site; the survey of a town pre|)aratory to planning 
sewer and watciworks systems and the planning of street pave- 
ments. 

The instrument should be titled with stadia wires for measur- 
ing horizontal distances, and this will usually prove a great conven- 
ience, resulting in savimr of both time and e.xnense. A steel 
tape should, however, be included in the equipment for field work, 
for the purpose of checking measurements with the stadia. In 
addition to the above there should' be ])rovided, the following 
equipment: 

Self readinf; level rod, capable of being read to hundredths of a foot. 

Hatchet. 

Marking crayon. 

2 or .'5 medium pencils, kept well sharpened. 

Plumb l)ob. 

Rubber eraser. 

Fortal)le turnint; jvoint. 

The mctlind of using the level rod in connection with the 
stadia for measuring distances has been fully discussed in Part II. 



PLANE SURVEYING 189 

The portable turning point will prove of great convenience 
and mav l>e made from a triangular ])iece of thin steel, with the 
corners turned down to ]iroject about one inch. 

If the level is to be used with the tape, the party will be 
made ii|) of the levelman, two tapemen and a rodnian, unless the 
nature of the work will ]iermit of the rodmaii carrying the rear 
end of the tape. If the stadia is used for measuring distances, 
only the rodnian will lie required in addition to the levelman. 
The levelman carries the note hook and enters into it all rod 
readings both for elevation and distances. These notes should be 
entered upon the left-hand page, the right-hand page being re- 
served for notes and sketches, which should be as full as possible. 
The leverman should cultivate the practice of calculating the ele- 
vations of the stations as the work progresses, at least of the 
turning points and bench-marks, in order that the results may be 
checked and errors discovered at once and corrected. If this work 
is left to be afterward carried out in the office, errors may be dis- 
covered that may require considerable time to locate and correct. 

If the area to be surveyed is, for instance, a i-eservoir site, it 
will be found most convenient to cover the area with a system of 
rectangles as shown in the figure, the parallel lines being spaced 
from 200 to 400 feet apart as may be most desirable. These lines 
should be run in with the transit, stakes being set at the inter- 
sections of the cross lines, or if the area is not very extended atid 
is comparatively level, by means of the level itself, the ])erpeii- 
dicular distances between the parallel lines being measured with 
the tape. 

These lines having been laid down, the next step is to estab- 
lish a system of bench-marks over the area. Begin by establishing 
a '• standard " bench-mark at some central point upon a permanent 
object, easily identified, and from thence radiate in all directions, 
returning finally to the original bench-mark for purposes of 
checking. Having located and satisfactorily checked the bench- 
marks, begin by running the level over all the lines running in 
one direction, as from A to B, back from C' to D and so on, taking 
rod readings at every fifty or one hundred feet, in addition to the 
readings at the stakes at intersections of cross lines. It is to be 
understood that stakes are not to be driven at the intermediate 



190 PLANE SURVEYING 

points. Next run the level over the lines at right angles to the 
former ones and in the same way, checking the levels at inter- 
sections. Advantage should be taken of every opportunity to 
check upon lieiich -marks ])revionsly located, and to establish 
others. 

In keeping the field records, the notes of the two sets of lines 
should be kept in separate books ; that is to say, if, for instance, 
one set of lines run north and south, and, therefore, the other east 
and west, the notes of the north and south lines should be entered 
in one set of books and the notes of the east and west lines in an- 
other set, and a note should be made of the direction in which a* 
line is run, as from north to south or from east to west. 

In conducting a survey for the preparation of a topographical 
maj) necessary to the design of a sewer or waterworks system, 
much the same method is to be followed, but now the streets and 
alleys take the place of the rectangular system referred to above. 
As before, all the streets and alleys running in parallel directions 
are to be gone over in a systematic way, readings being taken lifty 
or one hundred feet apart in addition to street and alley intersec- 
tions. (By street and alley intersections is intended the intersec- 
tions of the center lines, the lines of levels being run along these 
center lines.) If a fairly accurate maj) of a town is available, the 
distances iheasured with the tape along the center line of the streets 
and alleys will serve as a check upon the map. If, however, dis- 
crepancies occur or there is no map available, it will be necessary 
to use the transit for staking out street lines and for determin- 
ing the iclative directions of these lines. It follows that the 
topography of the ground between streets and alleys can only be 
approximated, but sufficient points accurately determined will 
have been established to permit the platting of a contour map, 
from which the system can be laid down. 

The ofKce work involved in the survey of an area, as above 
described, consists in preparing profiles of the level lines and pre- 
paring a jilat of the lines surveyed. From the profiles the contour 
points can i)e laid down in their proper position upon the plat, and as 
each point is laid down, its elevation should be noted in pencil, and 
after all the points have been platted, the points in the same contour 
line can be connected — preferably free-hand^ — producing the con- 



PLANE SURVEYING 1".H 



tour map. The scale to be adopted will depend upon the nature 
of the work, but should be as large as possible, consistent with the 
convenient handling of the map. 

Transit and Stadia. The inelhod by transit and stadia is of 
more general application than the preceding method, points being 
located by ''polar co-ordinates," that is to say, by direction and 
distance from a known point, the elevation being determined at 
the same time. 

Method of conducting fieI<L operations. If the area to be sur- 
veyed is small, the preceding method, based upon a system of 
rectangles, will prove satisfactory, and the elevations of the corners 
and salient points can be determined at the same time that the 
lines forming the rectangles are being laid down. Especial care 
should be taken to check the elevations of the corners. 

In making a survey for a sewer or a waterworks system, the 
transit and stadia method will be found efficient, especially in cases 
where no survey has ])reviously been made, the map, if it exists at 
all, having been compiled from the records in the (Jounty Record- 
er's office. The bench-marks necessary in a survey of this kind, 
however, should be established with the wye-level, and it may be 
desirable to determine the elevation of street intersections in the 
same way. 

If the area to be surveyed is too large, or of uneven topography, 
proceed as follows: Choose a point, as the intersection of two 
streets, the corner of a farm, or an arbitrary point conveniently 
located and drive a stake tirmly at this point, "witnessing" 
it from other easily recognized points or stakes. The trancit should 
be set over this point with the vernier reading zero, and the instru- 
ment pointed by the lower motion in the direction of the meridian. 
This may be the true meridian previously determined, the mag- 
netic meridian as shown by the needle, or an arbitrary meridian 
assumed for the purpose of the survey. It will generally be more 
satisfactory to run out a true meridian by means of the solar 
attachment, liut in any event the direction of the line taken as a 
meridian should be defined by stakes, firmly driven into the ground, 
and " witnessed " by stakes or other objects easily recognized. 
The elevation of the starting point, if not known, is assumed and 
recorded in the notebook. A traverse line should now be run, its 



192 PLANE SDKVEYING 

position and direction chosen with a view to obtaining from each 
station the largest possi])le number of pointings to salient features 
of the area under survey, and these pointings are taken while the 
instrument is set at any station, and before the traverse is com- 
pleted. 

The length of each course is measunnl with the stadia, and 
together with the azimuth and the vertical angle, it should be 
recorded in the notebook. The length, azimuth, and vertical angle 
of each course should be read from both ends to serve as a check. 
Tlie additional pointings taken from each course of a traverse are 
usually called " side shots", and for each there are required the 
distance, azimuth, and vertical angle. These will locate the point 
and determine its elevation. 

The method of using the stadia has already been quite fully 
discussed in Pai't II., and need not be repeated. 

The points selected for side shots should be such as will 
enable the contours to be platted intelligently a.d accurately upon 
the map of the area under survey. They should l>e taken along 
ridges and hollows and at all changes of slope. They should be 
taken at frequent intervals along a stream to indicate its course, 
or along the shore of a lake. It is usually re(juired that the 
location of artiticial structures, such as houses, fences, roads, etc., 
be determined that they may be mapjied in their proper position. 
Pointings, therefore, should be taken to all fence corners and 
angles, and to enough corners and anolcs of buildings, to peruiit 
of their being platted. Sufficient points should be taken along 
roads to determine theii' direction. Wooded lands, swamps, etc., 
may be indicated by pointings taken around their edges. In 
addition to the notes above described, the recorder should amplify 
the notes with sketches, to aid the memory in mapping. 

The traverse, of course, forms the backbone of such a survey, 
and the accuracy of the resulting topographical map will depend 
upon the degree of care bestowed u])on running the couroes. 
Over uneven ground, it is often desirable to run a secondary trav- 
erse from the first, for the more rapid and accurate location of 
points. 

The organization of a party will depend upon the nature 
of the country traversed and of the results required. Changes in 



PLANE SURVEYING 193 

the raake-np of parties, as given below, will suggest themselves 
for any special work. 

For economy and speed, tlie party for taking topography with 
transit and stadia w\]\ consist of a transitman or observer, a 
recorder in charge of the notebook, who should be capable of making 
such sketches as are necessary, and two to four men with stadia 
rods. The greater the distances to be traversed by the stadia men 
between points taken, the greater number the observer can woik 
to advantage, (^ne or two axemen njay be employed if clearing 
is to be done. 

The party may be reduced to two men — one to handle the 
instrument, record notes and make sketches, the other to carry the 
rod. 

The Plane Table and Stadia. The plane table is an instru- 
ment intentled for topographic purposes only and is used for the 
immediate mapping of a survey made with it, no notes of angles 
being taken, but the lines being platted at once upon the paper. 
The use of the plane table has been fully described. In topo- 
graphical work over an extended area, it may be used for filling in 
details, based upon a previous traverse made with a transit, or 
based upon a system of triangulation as will be described. Over 
small areas, the traverse itself may be run with the plane table 
and the details filled in at the same time. It is the standard in- 
strument of the United States Geological Survey and is largely 
used upon the United States Geodetic Survey. 

The points in favor of the plane table are : Eeonomy, since 
the map is made at once without the expense of notes and sketches; 
and as the mapping is all done upon the ground to be represented,- 
all of its peculiarities and characteristics can be correctly repre- 
sented. 

On the other hand, the plane table is an instrument useful 
only for taking topography ; the rodmen are idle while the map- 
ping is being done ; the instrument is more unwieldy than the 
transit, particularly upon difficult ground ; the record of the work 
for a long period is constantly exposed to accident ; the distortion 
of the paper with the varying dampness of air, introduces errors 
in the map ; while the area exposed makes it too unstable to use 
in high winds. 



194 PLANE SURVEYING 



The organization of a party for the taking of topography, 
tising the plane table, is much the same as with the transit and 
stadia ; however, on account of the weight of the instrument, 
means of transportation must be provided. 

A less number of rodmen can be employed than with the 
stadia, owing to the time required for maj)ping. 

An observer, a man to reduce stadia notes and sketch topog- 
raphy around points determined by intersection or stadia from 
the plane table station, and one rodman, will make the minimum 
working party, in addition to which, axemen and a team for trans- 
portation will be required. 

Photography. The following is taken from Gillespies Sur- 
veying iStaley). 

•• Photography has long been successfully employed by 
European engineers, notably those of Italy, for the purpose of 
taking topography. The Canadian Government has also employed 
it successfully in the survey of Alaska. 

The recommendation of this method is the trreat savincr of 
time in the field, while giving topographic features with all the 
accuracv re(juired for maj)S to be platted on a scale of 1 to 25,000. 

M. Javary states that the maximum error both for horizontal 
distances and elevations, using a camera with a focal leno;th of 
twenty inches and a microscope in examining the points, was 
only 1 in 5,000 as deduced from a number of cases. 

M. Laussedat, in his work, found that this method did not 
require more than one-third the time necessary by the usual 
methods. 

This makes it especially suitable in all mountainous regions, 
where eo much time is lost in getting to and from stations, that 
little is available for observations and sketching. 

A single occupation of a station with photographic apparatus 
would suffice to complete work that witii the ordinary methods 
would retjuire several days." 

Instruments. The ordinary camera may be used, if it is pro- 
vided with a level. A tripod head for leveling the instrument, 
and a roughly graduated horizontal circle for reading the direction 
of the line of sight, when photographing different parts of the 
horizon, are convenient attachments. 



PLANE SURVEYING 195 



A camera is soiuetitiies used upon a plane table, the reeurd 
of the work heiiiij made upon the paper in eouneetion with a set 
of radial lines drawn from the ])oint representing/ the station 
occupied. 

Many special forms of instrument conibinincr the camera and 
theodolite have been devised, some one of which should be iised 
if work of this kind is to be undertaken on a lariie scale. For a 
descrijition of these instruments, and a complete treatise on this 
suiiject. comprising a discussion of the requirements of the appa- 
ratus, the fundamental principle* of photography, methods of field 
work, forms of notes, reduction of notes and making of the map, 
together with the bibliography of the subject, see United States 
Coast and Geodetic Survey Report. 18U;5. Part II., Ajipendix 3. 

The camera tripod as ordinarily constructed is too unstable 
for purjioses of topograj)liic surveying, and it is desiiable to have 
a tripod constructed esp.ecially foi this class of work. Glass jilates 
are heavy and awkward to carry aside from their fragile nature. 
Cut films can be ])rocured in any of the standard sizes, and as 
they are light and stand ronoh handling and give ordinarily as 
good results as the glass jilates, they are to be preferred. Their 
cost is about double that of the ylass. 

TRIANGULATION. 

This method of surveying is sometimes called '• Ti'igonometi'ic 
Surveying" and sometimes '-Creodetic Surveying", though this 
latter is properly applied only when the area to be surveyed is so 
extensive that allowance must be made for the curvature of the 
earth. Since this instruction ])aper is devoted to Pl;\ne Surveying- 
only, the curvature of the earth v.-ill be neglected. 

Triangulation, or Triangular Surveying, is founded upon the 
method of determining the position of a jioint at the ape.x of a 
ti-iangle of which the base and two angles are measured. Thus in 
Fio;. l"2i) the leno-th of the base line AB is measured and the 
angles PAB and PBA are measured, from which can be calculated 
the lengths of the sides PxV and PE. This calculated length of 
PA will then be taken as the side of a second triangle, and the 
angles PAC and Pt'A measured, from which the other sides of 
the triangle can be calculated. By an extension of this principle, 



196 



PLANE SURVEYING 




Fig. 129. 



a field, farm, or a country can be surveyed by measuring a base 
line only, and calculating all of the other desired distances, which 
are made the sides of a connected series of imaginary triangles 
whose angles are carefuliv measured. 

Measuring the base line. For 
a base line, a fairly level stretch 
of ground is selected, as nearly as 
possible in the middle of the area 
to be surveyed, and a line from 
one thousand feet to one-half mile, 
or longer, is very carefully meas- 
ured. The ends of this line are 
marked with stone monuments or 
solid stakes. If the survey is of 
sufficient importance, the ends of 
the base line and the apexes of the 
triangles should be permanently 
preserved by means of stones not less than six inches square in 
cross-section and two feet long, these stones being set deep enough 
to be beyond the disturbing action of frost. Into the top of this 
stone should l>e leaded a copper bolt about one-half inch in diam- 
eter, the head of the bolt being marked with a cross to designate 
the exact point. The point may be brought to the surface by a 
])iumb.line for use in the survey. The location of each monument 
should be fully descril)ed with reference to surrounding objects of 
a permanent character, so as to be easily recovered for future use. 
The measurement of the base line for the areas of limited 
extent should be made with a precision of from one in five thousand 
to one in fifty thousand, depending upon the scale of the map, 
the ext';nt of the area under survey, and the nature and imj)ortance 
of the work. 

The two ends of the base line having been determined and 
marked, the transit is set over one end and a line of stakes ranged 
out between the two ends, esjiecial care being taken to make the 
alignment as perfect as possible. These stakes should be not less 
than two inciies square, driven firmly into the ground, preferably 
at even ta])e lengths apart, or at least at one-half or one-quarter 
tape lengths, center to center; the centers sho^Jfl be marked by 



PLANE SURVEYING 197 

tine Bcratclies iijiim strips of tin or zinc tacked to the top of the 
stakes. 

For oalinarv work the base line may he measured with a tape, 
notes being made of the temperature, pull, grade, and distances 
between supports, tlie tape having been previously standardized. 
For a degree of precision, such as is attempted upon the work of 
the United States Coast and Geodetic Survey, more refined methods 
are used, but as this properly belongs to geodetic surveying, it is 
unnecessary to consider it here. 

Measuring the angles. After establishing and measuring 
the baseline, ]>roniinent points are chosen for triangulation points 
or apexes of triangles, and from the extremities of the base line 
angles are observed to these points, care being taken to so choose 
the points that the angles shall in no case be less than 30^, nor 
more than 120". The distances to these and between these points 
are then calculated by trigonometi-ic methods, the instrument being 
then j)laced at each of these ne\y stations and angles observed from 
them to still more distant stations, the calculated lines being used 
as new base lines. This process is repeated and extended until the 
entire district included in the survey is covered with a network of 
"primary triangles " of as large sides as possible. One side of the 
last triangle should be so located that its length can be determined 
by direct measurement as well as by calculation; the accuracy of 
the work can thus be checked. Within these primary triangles 
secondary or smaller triangles are formed to serve as the starting 
points for ordinary surveys with the transit and tape, transit and 
stadia, plane table, etc., to fix the location of minor details. 
Tertiary triangles may also be formed. 

When the survey is not very extensive, and extreme accuracy 
is not required, the ordinai-y methods of measuring angles may be 
employed, (-)therwise there are two methods of measuring angles, 
called, respectively, the method of repetition and the method by 
continuous reading. When an engineer's transit is used for 
measuring angles, the method by repetition is the simplest and 
best and is carried out as follows : The vernier is preferably set 
at zero degrees and then by the lower motion turned upon the left- 
hand station; ^e lower motion is then clamped and the instrument 
turned by the*ihpper motion upon the right-hand station; the 



198 



PLANE SURVEYING 



upper motion is then clamped and the instrument turned by the 
lower motion upon the left-hand station; lower motion clamped 
and instrument again turned by upper motion upon right-hand 
station. This process is repeated as often as may be necessary to 
practically cover the entire circle of 300' and the circle is then 
read. This reading divided by the number of repetitions will give 
the value of the angle. 

Now reverse tlie telescope and repeat the observations 
described above, but from r'njht to left; the readings being taken 
in both directions to eliminate errors due to clamj)ingand unclamp- 
ing and personal errors due to mistakes in setting ujjon a station. 
The readings should be taken with the telescope both direct and 
reverse to eliminate errors of adjustments. Both verniers should 
be read in order to eliminate errors due to eccentricity of verniers, 
and the entire circle is included in the operation in order to elim- 
inate errors due to graduation. 

The second methoil, by continuous reading, consists in point- 
ing the telescope at each of tlu' stations consecutively, and reading 
the vernier at each pointing; the difference between the consecu- 
tive readings being the angle be- 

o o o 

tween the corresponding points. 
Thus in Fig. 130 with the instru- 
ment at zero, the telescope is first 
directed to A and the vernier is 
-C read; then to B, C, D, E, etc., in 
succession, the vernier being read 
at each pointing. The reading 
of the vernier on A, subtracted 
from that on B, will give the angle 
AOB and so on. It is necessary 
in this method, to read both to 
the right and to the left, and with the telescope both direct and 
inverted. Since each angle is measured on only one part of the 
limb, it is necessary after completing the readings once around 
and back, to shift the vernier to another part of the limb and 
repeat the readings in both directions, and with the telescope 
direct anil inverted. This is done as many times as there are sets 
of ri-adings. Each complete set of readings to right and left, with 




Fis. i: 



PLANE SURVEYING 199 



the telescope direct and inverted, gives one value for each angle. 

•The lengths of the sides of the triangles should be calculated 
with extreme accuracy in two ways if possible, and by at least two 
persons. Plane trigonometry may be used for even extensive 
surveys; for though these sides are really arcs and not straight 
lines the error under ordinary circumstances will be inappreciable. 

Radiating Triangulation. This method as is illustrated in 
Fig. 181 consists in choosing a con.spicuuus ])oint O, nearly in the 
center of the area to be surveyed. Other points as A, !>, (', I), 
etc., are so chosen that the signal at () can be seen from all of 
them, and that the triangles ABO, BCO, etc.. shall be as nearly 
equilateral as possible. Measure 
one side, as AB for example, 
and at A ineasure the angles 
OAB and OAG; at B measure 
the angles OB A and OBC; and 
so on around the polygon. Tlie 
correctness of these measure- 
meBts may be tested by the sum 
of the angles. It will seldom be 
the case, however, that the sum 
of the angles will come out just 
even, and the angles must then 
be adjusted, as will be explained '^' 

later. The calculations of the lengths of the unknown sides are 
readily made by the usual trigonometric methods; thus in the tri- 
angle AOB, there are given one side and all of the angles of the 
triangle from which to calculate AO and BO. Similarly all of 
the triangles of the polygon may be solved, and finally the length 
of OA may be measured and compared with the calculated length, 
as found from the first triangle. 

A farm or field may be surveyed by the previously described 
method, but the following plan will often be more convenient : 
Choose a base line as AB within the field and measure its length. 
Consider first the triangles which have AB for a base, and the 
corners of the field for vertices. In the triangle ACB for example 
(see Fig. 132), we measure the angles CAB and CBA and the 
length of the base line AB. We can therefore calculate the length 




200 



PLANE SURVEYING 




of AC ami BC. Next consider the field as made up of triangles 
with a eoimnoii vertex A. In eaeh of them, two sides and the 
included anirle are given, to find the third side. If now the point 
B at the other end of the base line be taken for a common vertex. 
a check will l)e ol-.tained upon the work. 

A Held or a farm or any inaccessible area such as a swamp, 
a lake, etc.. may be surveyed without entering it. For a farm or 
any area jicrmitting unobstructed vision, it will yidy be necessary 

to choose a base line AB, from 
which all of the corners of the 
farm, or all of the salient points 
of the area, can be seen. Take 
their bearings, or the angles be- 
tween the base line and their 
directions. The distances from- 
A and B to each of them can be 
calculated as described, and the 
figure will then show in what 
manner the content of the field 
is tile difference between the contents of the triangles having A 
or 1) for a vertex, which lie outside of it, and those which lie 
jiarily within the field and partly outside of it. Their contents 
can be calculated, and their difference will be the desired content. 
See Fig. 13;!. l-^vidently the entire area included between the cor- 
ner.s of the ticKl and the base line is the sum of the triangles A2B, 
2B."! and ;5B4. Subtracting from this sum the areas of the tri- 
angles 12A1, lAB, IBti, uCB and 5B4. there will remain the 
recjuired area of the field, 128-f5ti. 

in all of the operations which have been explained, the posi- 
tion of a jioint has l)een determined by taking the angles, or bear- 
ings, of two lines passing from the two ends of a base line to the 
unknown point, but the same determination may be effected 
inversely by taking from the point the bearings by compass of the 
two ends of the base line or any two known points. The uid<uown 
])oint will then be fixed by plotting from the two known jioints, 
the opj)Osite bearings, for it will be at the intersection of the lines 
thus determined. 



PLANE SLRVEYIXO 



201 



The determi nation of :i point by the method founded on the 
. intersection of lines, lias the serious defect that the point sighted 
to will he very iiuietinitely determined if the lines which tix it 
meet >\t a very acute or a very obtuse angle, ■which the relative 
position of the points ol)served from and to often render unavoid- 
able. Intersections at right 
anLjIes should therefore be 
souD-ht for, so far as other con- 
siderations will ]iermit. 

Adjusting the Triangle. 
All of the auifles of a ijiveii tri- 
angle are measured. If but two 
have been measured, and the 
third computed, the entire error 
of measurement of the two angles 
will be thrown into the third 
angle. It will be found, ujion 
adding together the measured angles of a triangle, that the sum of 
the three angles is almost invariably more or less than ISO . With 
the engineer's transit the error should be less than one minute. 
If there is no reason to suppose that one angle is measured more 
carefully than another, this error should be divided equally among 
the three angles of the triangle, and the ca/^rected angles are used 
in computing the azimuths and lengths of the sides. This distri- 
bution of the error is called "adjusting"' the triangle. With the 
large systems of extensive geodetic surveys much more elaborate 
methods are employed, since a large number of triangles must be 
adjusted siiuultaneously so that they will all be geometrically con- 
sistent, not only each by itself, but one with another. 




I'^itr. i:«. 



INDEX 



Page 

Abney clinometer 31, 1S4 

hand-level 31 

Adjustments of 

axis of bubble-tube 48 

compass 73 

dumpy-level 50 

vertical axis 49 

■tt-ye-level 47 

Alidade 175 

Alignment, obstacles to 1 53 

Altitude of star 1 40 

Annual variation 69 

Axis of bubble-tube, adjustment of 4S 

Axis, polar, adjustment of 143 

Azimuth 91 

of Polaris at elongation , . 131 

Balancing tlie survey .S4 

Base measurement. .. . 162, 165, 171, 196 

measuring apparatu.s 166 

errors in 1 06 

Bearing of one line to another 77 

Bench mark 58 

Boston rod 41 

Calculating the content 85 

Camera used in surveying 194 

Care of the level 55 

Chaining on slopes 10 

Change bearings 81 

Chromatic aberration 47 

Clinometer 31 , 1S4 

Collimation, line of 46 

Compass 70 

adjustment of 73 

construction of 70 

magnetic needle 71 

sights * 72 

tangent scale 72 

use of 74 

Compensated rods. 166 

Correction lines 162 



204 INDEX 

Page 

C'ross-luiirs, replacing 49 

Cross-sect ion rod 41 

Cross-sectioning 01 

Declination , 147 

Deflection angles 112 

Diurnal variation . 09 

Division of land 93 

Doulile longitudes SO 

1 )unipy -level . . 50 

adjustments of 50 

Engineer's transit 104 

Fariu surveying ; 79 

change bearings ■ 81 

field notes SO 

intersections, method of 79 

progression, method of 79 

proofs of accuracy 80 

radiation, method of 79 

Field notes 80, 118 

keeping of 22 

Field work of measuring areas 18 

Geodetic surveying 3, 195 

Gradienter ■ 133 

used as telemeter. 134, 136 

used as level 135 

used as grade-nieasurcr 135 

Guide meridians . . 163 

Guntcr's chain . . 5 

Gunler's measure 6 

Gurley binocular 52 

Gurley monocular hand-level 53 
Hand-levels 

Abney 31 

Locke's . . 29 

Iced bar 166 

Instrumental parallax. 46 

Instruments, surveying .' 43 

Intersections, method of ■ 79, 181 

Isogonie lines 70 

Keejiing field notes.. . 22 

Land measure 6 

Latitude 82, 140, 146 

coefficients 148 

Latitude ditTeience ._ 82 

Latitudes jind depaituies 82 

Level 

to adjusi 73 

care of 55 

setting up 53 



INDEX 205 

Page 

Level bubble 26 

Leveling 56 

Leveling rod 33 

Line running .14, 153 

correction 162 

Line of coUimation 46 

Lines, niea.surenient of 4 

Locke's hand-level 29 

Longitude difference. . 82 

Longitude of a point " 82 

Magnetic declination 69 

Magnetic needle 71 

Maps, topographic. 181 

Meander line 117 

Measurement, base, see Base measurement 

Measurement of lines -1 

Meridian plane ('>9 

Meridian, true , 95, 115 

Meridian, laying out with compass 96 

with transit 1,39 

prime or principal 162 

guide .• 163 

Minus-sight 58 

\eedle, to adjust. . 73 

Needle, to the dip, to adjust 73 

New York rod 39 

North Star, see Polaris 

Offsets and tic-lines 19 

Omissions, supplying 1 57 

Parallels, standard 162 

Perpendiculars, erection of 14, 119 

Photography in surveying 191 

Plane surveying 3 

Plane-table, construction of 1 74 

uses of 1 75, 177 

adjustment 176 

in topographical surveying 193 

Plug 5S 

Plus-sight 5S 

Polar axis, adjustment of 143 

Polaris, used in laying out meridian 95, 139 

Precise spirit level 52 

Prime meridian 1 62 

Prismatic compass 73 

Profile leveling 59 

Progression, method of 79, 180 

Public land surveying 160 

Radiating triangulation 199 

Ranges 160, 161 



20C INDEX 

Page 

Hanging poles 42 

Refraction, effects of • 147 

correction ■ 150 

Relocation 76 

Replacing cross-hairs. .49 

Resurveys i'l 

Sections Iti", 1(>2 

Secular variation. . . .09 

"Setting up" the level ."):! 

Sight -vanes, to ailjusi .7:5 

Solar transit Ml 

adjustments It:? 

uses of H 5 

Spherical aberration. 17 

Stadia 120 

use of in field 1 2.5 

in topograjihical surveying.. 191, 193 

Stadia rods 127- 

Standard parallels. . 1(;2 

Star, altitude of .140 

Stretchers 1 (is 

Supplying omissions. . 90 

Surveying 

geodetic 3, 195 

with instruments 5 

plane 3 

public land lliO 

topographical. . . LSI 

trigonometric, or triangulation 19.5 

Surveying instruments . 43 

Surveyor's tran.sit ... 104 

Tacliynieter 104 

Tape" 8 

use of 9 

Telemeter 134, 1.36 

Testing a survey by latitudes .and departures 83 

Theodolite : 104 

Tie-lines 19 

Time, determination of 140 

Time of elongation and culmination of Polaris 131 

Topographic.il surveying 181 

Towaiships. .100, 161 

Transit 97 

construction of . . 97 

engineer's 104 

to "set-up" 110 

surveyor's 104 

laying out meridian 139 

solar 141 



INDEX L'(>7 

Page 
Transit 

;iiljustiiieiits 1-13 

ill topognipliital surveyins 191 

Transif-tlieodolitc 104 

Traversing: 1 1 1. ISO 

Triaiifiulatioii. Inl, 195 

measurement of base line. ... ... 196 

measurement of angles. . 197 

radiatiuf; 1!I9 

adjusting the triangle 201 

I'riso'iomelrie surveying 195 

True meridian 95, 145 

Turning point 58 

r. S. geodetic survey. . 132 

r. S. public land surveying KiO 

T'se of .stadia in field 125 

Variation ■ <>9 

Vernier 2.S 

Vertical axis, adjustment of 19 

Wye level IH 

adjustments of 17 






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